The graph of this function is given again on the left in Figure10.2.2. }\) A partial derivative is a derivative of an appropriate trace.). For additional information on the 2021 OHC, please see the paper titled Another Record: Ocean Warming Continues through 2021 despite La Nia Conditions. The units used in this indicator are degrees Celsius (C) and degrees Celsius per decade (C/decade). Recall that the difference quotient \(\frac{f(a+h)-f(a)}{h}\) for a function \(f\) of a single variable \(x\) at a point where \(x=a\) tells us the average rate of change of \(f\) over the interval \([a,a+h]\text{,}\) while the derivative \(f'(a)\) tells us the instantaneous rate of change of \(f\) at \(x=a\text{. For the month as a whole, Spain had below-average July precipitation, receiving only 57% of normal July precipitation. State the limit definition of the value \(I_H(94,75)\text{. This means that a single degree Celsius equals 1.8 degrees Fahrenheit. This was also the earliest a maximum temperature of 25.0C (77.0F) was set in Beijing. Twelve of India's 15 warmest years have occurred since 2006. The heavy rain prompted severe floods and damaged over 100 homes. The years 2010 and 2016 tied as Africa's warmest year on record at 1.44C (2.59F) above average. Another great irony is that many countries with the coldest climates, such as Canada, Sweden, Germany, and the UK, are the most concerned about warming. Monthly temperatures were above average for Africa during 2021. \frac{\partial f}{\partial y}(a, b) = f_y(a,b). Based in one of the world's most exciting capital cities, London Met is home to a diverse community of inspiring and determined learners, teachers and innovative thinkers., Our vibrant, diverse, metropolitan university is located at the heart of one of the most exciting cities in the world. These changes in leaf cover can be detected by satellite, particularly in deserts and savannas where the cover is less complete than in wet locations, according to Randall Donohue, the CSIRO research scientist. The IPCC AR6 presents a strong body of scientific evidence that it is unequivocal that humans have caused the earths climate to warm, with a likely human contribution of 0.8 to 1.3 degrees Celsius to global mean temperature since the late 1800s. The ocean heating is irrefutable and a key measure of the Earth's energy imbalance: the excess greenhouse gases in the air trap more heat inside the climate system and drives global warming. This correspondence generally fits with the "wet getting wetter, dry getting drier" scenario. The nadir in body temperature usually occurs at about 4 a.m. and the peak at about 6 p.m. \end{equation*}, \begin{equation*} Further east positive anomalies dominate the norther part of South America and the Atlantic ITCZ. Across Canada there is fairly consistent dryness, except in the last quarter of the year. In 2015, while attending the COP (Conference of the Parties) in Paris, I offered a public bet for $100,000 in a broadcast media release which went out on more than 200 media feeds, that by 2025 global CO2 emissions would be higher than in 2015. Find the partial derivative \(f_y(1,2)\) and relate its value to the sketch you just made. According to Moore, nearly all commercial greenhouse farmers worldwide buy CO2 to inject into their greenhouses to realize up to 60 percent higher crop yields. And CO2 is lower now than in more than 95 percent of Earths history. Over Africa and South America the typical La Nia patterns vary during the year but are generally consistent during the year. By August 11, tropical storm Fred made landfall in Hispaniola. Left: Graphs \(f(t)= M(0.03, t)\text{. Korea also set a new national February temperature when the city of Pohang had a maximum temperature of 24.9C (76.8F). Europe had its warmest year on record at 2.16C (3.89F) above average, surpassing the previous record set in 2018 by 0.28C (0.50F). Gulab brought torrential rains to parts of India, causing significant damages, such as toppling power lines, flooding roads, and damaging homes. Temperature anomalies are presented relative to a pre-industrial period between 1850 and 1899 (the beginning of instrumental temperature records). This chapter frames the context, knowledge-base and assessment approaches used to understand the impacts of 1.5C global warming above pre-industrial levels and related global greenhouse gas emission pathways, building on the IPCC Fifth Assessment Report (AR5), in the context of strengthening the global response to the threat of climate change, sustainable development and However, no land or ocean areas were record cold for the year. ~\mbox{feet per radian} . Negative 40 degrees Fahrenheit (-40 F) is equal to negative 40 degrees Celsius (-40 C). Most of the feedbacks can show both continuous responses and tipping point behavior in which the feedback process becomes self-perpetuating after a critical threshold is crossed; subsystems exhibiting this behavior are often called tipping elements ( 17 ). Also, about 75% of the Paraguay river basin was also suffering some type of drought as of August 3. \newcommand{\vm}{\mathbf{m}} Across western Canada, the warm and dry conditions during the end of the month contributed to the development of numerous wildfires in the region. The station in Mexicali, located in northwestern Mexico, recorded a maximum temperature of 50.4C (122.7F). Now we consider the first-order partial derivatives in context. The yearly temperature for North America has increased at an average rate of 0.13C (0.23F) per decade since 1910; however, the average rate of increase is a little more than twice as great (+0.29C / +0.52F per decade) since 1981. For additional information on the 2020 OHC, please see the paper titled Upper Ocean Temperatures Hit Record High in 2020. Lack of snow across Patagonia was also reported, with some locations reporting their lowest values since 2000. During the last week of June, an extreme heat wave affected much of the northwestern contiguous U.S. and western Canada with maximum (daytime) temperatures surpassing 38.0C (100F), which is not typical for the region. He received the Best Scientist and Engineer Award from Korea Science Foundation in 2007 and a Presidential Commendation in 2013. The years 20132021 all rank among the ten warmest years on record. Moore said the young generation today is taught that humans are not worthy and are destroying the earth. \end{align*}, \begin{equation*} }\) To recap, we have now arrived at the formal definition of the first-order partial derivatives of a function of two variables. By holding \(x\) fixed and differentiating with respect to \(y\text{,}\) we obtain the first-order partial derivative of \(f\) with respect to \(y\). \displaystyle \frac{x2^tz^3}{1+x^2}.\). Much of North America had temperatures that were at least 3.0C (5.4F) below average. Hong Kong had very wet conditions during October 2021, receiving over six times the monthly normal of 100.9 mm (4.0 inches). + \frac{\partial}{\partial x}[2y] = y\cdot 2x - y Suppose we take out an $18,000 car loan at interest rate \(r\) and we agree to pay off the loan in \(t\) years. However, for the first three months of the year, during El Nio conditions, there is the usual excess rainfall in the central Pacific along the Equator and generally drier than normal conditions over the Maritime Continent. The 19012000 average combined land and ocean annual temperature is 13.9C (57.0F), the annually averaged land temperature for the same period is 8.5C (47.3F), and the long-term annually averaged sea surface temperature is 16.1C (60.9F). Over the latitude band from 50N-50S the area-weighted correlation between the trend field and the 2020 anomaly field is +0.30, the positive correlation indicating that general reinforcement in 2020 of the longer-term changes occurring in the global precipitation pattern. Full 2021 report In other words, if Microsoft owned Call of Duty and other Activision franchises, the CMA argues the company could use those products to siphon away PlayStation owners to the Xbox ecosystem by making them available on Game Pass, which at $10 to $15 a month can be more attractive than paying $60 to $70 to own a game outright. Sucrose, a disaccharide, is a sugar composed of glucose and fructose subunits. November was Oceania's coldest month in 2021, with a temperature below average and Oceania's coldest November since 1999. This was also Africa's 45th consecutive year with temperatures, at least nominally, above average. C(x,y) = \frac{25xy+25}{(x-1)^2 + (y-1)^2 + 1}. Further, expansion due to increased ocean heat contributes to sea From 1979 to 1986, Moore served as the Director of Greenpeace International, a driving force shaping the groups policies and directions. Averaged across land and ocean, the 2021 surface temperature was 1.51 F (0.84 Celsius) warmer than the twentieth-century average of 57.0 F (13.9 C) and 1.87 F (1.04 C) warmer than the pre-industrial period (1880-1900). Given a function \(f\) of the independent variables \(x\) and \(y\text{,}\) what do the first-order partial derivatives \(\frac{\partial What information does \(f'(4)\) tell us about our car loan? and Ph.D. in Environmental Science from Rutgers University (New Brunswick, New Jersey) in 1983 and 1985. We are still in the Pleistocene Ice Age no matter how the climate alarmists wish to deny this.. Europe's annual temperature has increased at an average rate of 0.15C (0.27F) per decade since 1910; however, it has tripled to 0.45C (0.81F) since 1981. \newcommand{\vj}{\mathbf{j}} The following analysis is based upon the Global Precipitation Climatology Project (GPCP) Interim Climate Data Record. f(x,0.6) = \frac{\sin(1.2)}{32}x^2, Your monthly car payment in dollars is \(P = f(P_0,t,r)\text{,}\) where $\(P_0\) is the amount you borrowed, \(t\) is the number of months it takes to pay off the loan, and \(r\) percent is the interest rate. The Indian Ocean also reflects the La Nia effect with positive anomalies in the east and dry conditions in the west, extending into eastern Africa, but with positive anomalies over South Africa. Peterson, T.M. Austria, as a whole, had its coldest year since 2010, with a temperature that was 0.1C (0.2F) below the 19912020 average. \newcommand{\vw}{\mathbf{w}} A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. \end{equation*}, \begin{equation*} Moreover, if we fix the angle \(y = 0.6\text{,}\) we may view the trace \(f(x,0.6)\) as a function of \(x\) alone, as seen at right in Figure10.2.2. It is a bit like a Ponzi scheme in the stock markets, Moore added. 9(4), 138; doi:10.3390/atmos9040138. Today, the left has adopted many policies that would be very destructive to civilization as they are not technically achievable. Conson made landfall across central Philippines on September 6, bringing strong winds and heavy rain that prompted floods in low-lying communities. Parts of eastern Mexico had twice their June normal precipitation. Really cold Arctic air moved towards the mid-latitudes during the first half of February. They are primarily focused on creating narratives, stories, that are designed to instill fear and guilt into the public so the public will send them money.. The yearly temperature for South America has increased at an average rate of 0.14C (0.25F) per decade since 1910; however, the average rate of increase is nearly double that value (0.23C / 0.41F) since 1981. However, that record only lasted one day since the record was yet again broken the following day when temperatures soared to 25.6C (78.1F). Drought over these land areas in the Americas was a key attribute of 2020. Africa's 10 warmest years have all occurred since 2005, with the five warmest occurring since 2010. }\), (a) Using difference quotients with \(\Delta x = 0.1\) and \(\Delta y = 0.1\text{,}\) we estimate. State respective direction vectors for the two lines determined in (b) and (c). According to Argentina's Servicio Nacional Meteorolgico, minimum temperatures were above average during the month, with several locations setting new minimum temperatures on record. Other features mentioned also reverse. }\), Determine \(f_x(x,y)\) and \(f_y(x,y)\text{. It is paramagnetic and thus essentially unaffected by static magnetic fields. Of note, Montreal had a maximum temperature of 36.6C (97.9F) on May 27, 2020the hottest May temperature and the second highest ever on record for Montreal. Once again, the derivative gives the slope of the tangent line shown on the right in Figure 10.2.3.Thinking of the derivative as an instantaneous rate of change, we expect that the range of the projectile increases by 509.5 feet for every radian we increase the launch angle \(y\) if we keep the initial speed of the projectile constant at 150 feet per second. Oceania's 10 warmest years have occurred since 1998, while the five warmest year have all occurred since 2005. [Left-leaning] political activists in North America and Europe changed Greenpeace from a science-based organization to a political fundraising organization, Moore said. According to Moore, our digestive system can tell the difference between food and plastic or tiny particles of sand. Suppose the interest rate is fixed at \(3\%\text{. Figure 10.2.5. 0}\frac{f(150, 0.6+h) - f(150, 0.6)}{h}. The following months of March and June through October ranked among North America's top 10 warmest for each respective month. With a national mean temperature departure from average of 1.15C (2.07F) above the 19611990 average. Not once has this come true. 5. Argentina's national temperature for 2021 ranked among the top six warmest years on record, with a national temperature departure of 0.5C (0.9F) above average. This surpassed the previous decadal record (20012010) value of +0.62C (+1.12F). Explain the meaning of the function \(g\text{.}\). Asia's 10 warmest years have occurred since 2002, while the five warmest years have all taken place since 2007. Here \(C\) is the speed of sound in meters/second, \(T\) is the temperature in degrees Celsius, \(S\) is the salinity in grams/liter of water, and \(D\) is the depth below the ocean surface in meters. 4y}\) at the point \((x,y) = (4, 1)\text{. A. J. The La Nia composite has a dry feature over the eastern Pacific extending across all the southern states with positive anomaly across Canada; however, the pattern for 2021 has a corresponding feature in the eastern Pacific, but over the continent things are very different. }\) Given that \(f(0, 9) = 1\text{,}\) use this information to estimate the value of \(f(1, 10)\text{. During his 15-year tenure, Greenpeace became the worlds largest environmental activist organization. In Leibniz notation, observe that, To see the contrast between how we calculate single variable derivatives and partial derivatives, and the difference between the notations \(\frac{d}{dx}[ \ ]\) and \(\frac{\partial}{\partial x}[ \ ]\text{,}\) observe that. This is true across the tropical Pacific, where the patterns are very alike and even extending into the mid-latitude parts of that ocean in both hemispheres. Also, as discussed below, extreme precipitation and drought events occurred across the world. Chanthu was responsible for destroying infrastructures across the Batanes Islands, as well as toppling poles and trees, causing power outages. The environmental movement has become more of a political movement than an environmental movement, he said. }\) Sketch the graph of \(g\) on the right of Figure10.2.1. The yearly temperature for North America has increased at an average rate of 0.13C (0.23F) since 1910; however, the average rate of increase is a little more than twice as great (0.29C / 0.52F) since 1981. Following a record warm year (2020), 2021 was characterized by above-average monthly temperatures throughout the year. \newcommand{\va}{\mathbf{a}} \newcommand{\vR}{\mathbf{R}} (Courtesy of Patrick Moore), Prominent scientist backs up claim that there is no climate emergency. Cristobal brought torrential rains that prompted floods and landslides across southern Mexico and parts of Guatemala. The record is clear that the world has been warming since about the year 1700, 150 years before we were using fossil fuels. The year 2021 also marks North America's 25th consecutive year with temperatures, at least nominally, above average. Vegetation across these areas was damaged due to the really cold temperatures. The year 2020 also marked the 36th consecutive year with temperatures above average across Oceania. In fact, this past winter in the Arctic saw an expansion of ice from previous years, and Antarctica was colder during the last winter than in the past 50 years.. Extended Reconstructed Sea Surface Temperature Version 4 (ERSST.v4). }\), Locate, if possible, one point \((x,y)\) where \(f_y(x,y)>0\text{. Cyclone Seroja formed in the eastern Indian Ocean basin early in the month and crossed the coast of Western Australia on April 11. Of note, June 2021 was North America's warmest June on record with a temperature that was 2.0C (3.6F) above average, surpassing the previous record set in 2016 by 0.33C (0.59F). }\), Evaluate each of the three partial derivatives at the point where \(T=10\text{,}\) \(S=35\) and \(D=100\text{. Features of the same sign as in the trend map are noted generally in the features in the 2021 anomalies (repeated in bottom panel of Fig. The rains helped improve drought on the island. During 2021, the heating was distributed throughout the world's oceans, with record-high heat across the North Atlantic Ocean, the North Pacific Ocean, and Mediterranean Sea. Plots for contours of \(g\) and \(h\text{. Find the partial derivatives \(C_T\text{,}\) \(C_S\) and \(C_D\text{. This property, called isochronism , is the reason pendulums are so useful for timekeeping. Mexico set a new August maximum temperature record on August 3, 2021. Figure 10.2.1. w = \sqrt{4 r^2 + 3 s^2 + 7 t^2} He co-founded Greenpeace in 1971 and served as president of Greenpeace Canada for nine years. On a certain day, at 1 p.m. the temperature is 92 degrees and the relative humidity is 85%. This is confirmed by the La Nia composite (Fig. It includes 12 core chapters and an online interactive atlas Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. State the units in which each of the partial derivatives, \(C_T\text{,}\) \(C_S\) and \(C_D\text{,}\) are expressed and explain the physical meaning of each. Thinking of the derivative as an instantaneous rate of change, we expect that the range of the projectile increases by 509.5 feet for every radian we increase the launch angle \(y\) if we keep the initial speed of the projectile constant at 150 feet per second. EXCLUSIVE: Greenpeace Founder Patrick Moore Says Climate Change Based on False Narratives. }\) Using this information, sketch a possibility for the contour \(g(x,y)=4\) passing through \((2,2)\) on the left side of Figure10.2.9. }\) The values of the function on a few of the contours are indicated to the left of the figure. In fact, the polar bear population has increased from 6,000 to 8,000 in 1973 to 30,000 to 50,000 today. (b) Is \(\partial P /\partial r\) positive or negative? }\), Estimate the partial derivatives \(f_x(-1,2)\) and \(f_y(-1,2)\text{. As with the partial derivative with respect to \(x\text{,}\) we may express this quantity more generally at an arbitrary point \((a,b)\text{. Already, the planets temperature has risen by 1 degree centigrade. Peterson, T.M. It is provided courtesy of the GPCP Principal Investigator team at the University of Maryland. Significantly above-average annual precipitation occurred across northern South America, eastern Europe, western and eastern Australian coast, as well as parts of southern Asia. The lists do not show all contributions to every state ballot measure, or each independent expenditure committee formed to support or The year 2021 was the 11th consecutive year with a temperature above average. \newcommand{\vC}{\mathbf{C}} Further, expansion due to increased ocean heat contributes to sea 8.74~\mbox{feet per feet per second} , These tropical La Nia features in 2021 helped to fuel frequent flood conditions, for example, in Indonesia and Malaysia and surrounding countries and northern South America and eastern Brazil. }\) On the left side of Figure10.2.5, draw the graph of the trace with \(y=2\) around the point where \(x=1\text{,}\) indicating the scale and labels on the axes. f_y(a,b) = \lim_{h \to 0} \frac{f(a,b+h) - f(a,b)}{h} \end{equation*}, \begin{equation*} Only look at the looming energy crisis in Europe and the UK, which Putin is taking advantage of. 4) showing stronger La Nia-type patterns in the early and late months and weaker, but still discernible, such patterns in mid-year. Thinking of this derivative as an instantaneous rate of change implies that if we increase the initial speed of the projectile by one foot per second, we expect the horizontal distance traveled to increase by approximately 8.74 feet if we hold the launch angle constant at \(0.6\) radians. And this majority are mainly scientists paid by politicians and bureaucrats, media making headlines, or activists making money. With a yearly continental average temperature of 1.19C (2.14F) above average, Africa had its fourth warmest year (tied with 2015) in the 111-year record. }\), If \(f(x,y) = \displaystyle\frac{xy^2}{x+1}\text{,}\) find the partial derivatives \(f_x\) and \(f_y\text{. The following information was compiled from previous NCEI monitoring reports and public reports by National Hydrometeorological Services (NHMSs; peers of the U.S. National Weather Service). He said when elements (atoms) combine with each other to form compounds (molecules), they always have very different properties than the elements they are made from. The yearly temperature for South America has increased at an average rate of 0.14C (0.25F) per decade since 1910; however, the average rate of increase is nearly double that value (+0.25C / +0.45F per decade) since 1981. Before impacting portions of the southern and northeastern U.S., Ida also caused significant damage to parts of Cuba, by destroying homes and bringing down power lines. Over North America and surrounding oceans on both sides present a more complicated pattern, at least compared to the La Nia composite. [And] CO2 is a molecule that contains carbon and oxygen and is an invisible gas that is the primary food for all life. North America had its seventh warmest year on record with a temperature that was 1.40C (2.52F) above average. The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses level rise. y\frac{\partial}{\partial x}[x^2] - The following table lists the global combined land and ocean annually averaged temperature rank and anomaly for each of the 10 warmest years on record. \end{equation*}, Interpretations of First-Order Partial Derivatives, Using tables and contours to estimate partial derivatives, Active Calculus - Multivariable: our goals, Functions of Several Variables and Three Dimensional Space, Derivatives and Integrals of Vector-Valued Functions, Linearization: Tangent Planes and Differentials, Constrained Optimization: Lagrange Multipliers, Double Riemann Sums and Double Integrals over Rectangles, Surfaces Defined Parametrically and Surface Area, Triple Integrals in Cylindrical and Spherical Coordinates. \newcommand{\vzero}{\mathbf{0}} \ 1700 was the peak of the Little Ice Age, which was very cold and caused crop failures and starvation. According to preliminary reports, close to 400 people died and over 1,000 were injured due to the storm. If we evaluate this quantity at \(y=0.6\text{,}\) we have. National High and Low Temperature (for the contiguous United States) NWS Weather Prediction Center, College Park, MD Issued 2 pm EDT Tuesday, November 1, 2022 High Temperature for Monday, October 31, 2022 (as received by 2 pm EDT November 1) 94 at 4 miles southeast of Sebring, FL Low Temperature for Tuesday, November 1, 2022 (as received by 2 pm However, Fred's remnants caused torrential downpours across the southeastern contiguous U.S. Parts of western North Carolina had over 12 inches (305 mm) of rain. (b) Using difference quotients with \(\Delta x = 0.01\) and \(\Delta y = 0.01\text{,}\) we find better estimates: Determine the sign of \(f_x\) and \(f_y\) at each indicated point using the contour diagram of \(f\) shown below. Part I: Upgrades and Intercomparisons. The January 2021 temperature for Asia was above average at +0.32C (+0.58F), marking Asia's coldest January since 2012. }\) In fancy terms, it is the first Taylor approximation. The years 20132021 all rank among the ten warmest years on record. ) and a kelvin symbol that is followed by a superscripted negative 1 exponent. Moore said carbon neutrality is a political term, not a scientific one. Only the years of 2016 (second warmest) and 2020 (warmest) were warmer. Find the partial derivatives of the function, \(\frac{4r}{\sqrt{4r^{2}+3s^{2}+7t^{2}}}\), \(\frac{3s}{\sqrt{4r^{2}+3s^{2}+7t^{2}}}\), \(\frac{7t}{\sqrt{4r^{2}+3s^{2}+7t^{2}}}\). According to India's Meteorological Department, India's annual temperature departure of +0.29C (+0.52F) was the eighth highest since national records began in 1901. How are the first-order partial derivatives of a function \(f\) of the independent variables \(x\) and \(y\) defined? }\) Many [so-called] environmental leaders were now saying that humans are the enemies of the Earth, the enemies of Nature. I could not accept that humans are the only evil species. C=1449.2+4.6T-0.055T^2+0.00029T^3+(1.34-0.01T)(S-35)+0.016D. However, after the month of February, temperatures were at 0.80C (1.44F) or higher for the remaining months of 2021. Moore received his Ph.D. in Ecology from the University of British Columbia in 1974 and an Honorary Doctorate of Science from North Carolina State University in 2005. The carbon in our atmosphere has created a blanket of gas that traps heat and is changing the worlds climate. Determine the equation of the plane that passes through the point \((2,1,f(2,1))\) whose normal vector is orthogonal to the direction vectors of the two lines found in (b) and (c). Climatologically, Beijing's average maximum temperature in February is 4.0C (39.2F). In 1991, Moore founded Greenspirit, a consultancy focusing on environmental policies, energy, climate change, biodiversity, genetically modified food, forests, fisheries, food, and resources. The following table lists the global combined land and ocean annually averaged temperature rank and anomaly for each of the 10 warmest years on record. Figure 4 (top panel) shows the time history of the anomaly values in these zones (ocean and land combined) showing an increase in the low-latitude zone and a decrease in the mid-latitude peak. This is not disputed, Moore said. The year 1998 is no longer among the 10 warmest years on record, currently ranking as the 11th warmest year in the 141-year record. }\), \(\displaystyle \frac{\partial f}{\partial x}(4, 1) =\), \(\displaystyle \frac{\partial f}{\partial y}(4, 1) =\). It is simply wrong to call CO2 carbon. Carbon is an element that is what diamonds, graphite, and carbon black (soot) are composed of. Predictions that the world is coming to an end have been made for thousands of years. Lee Yun-Jeong is an Epoch Times reporter based in South Korea. Mosquitoes have a slender segmented body, one pair of wings, one pair of halteres, three pairs of long hair-like legs, and elongated mouthparts. \end{equation*}, \begin{equation*} }\) We can use these same concepts to explain the meanings of the partial derivatives in context. \end{equation*}, \begin{equation*} During the last two weeks of February, a warm spell affected East Asia with several locations experiencing new maximum temperature records. The wind chill, as frequently reported, is a measure of how cold it feels outside when the wind is blowing. + \frac{d}{dx}[3] = 3\cdot 2x - 2,\\ Once again, the derivative gives the slope of the tangent line shown on the right in Figure10.2.3. }\) Estimate the values of \(I(91,80)\) and \(I(92,78)\text{.
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