Brief Applied Calculus
Geoffrey C. Berresford
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This book uses intriguing real-world applications to engage readers' interest and show them the practical side of calculus. Its many applications are related to finance, business, and such general-interest topics as learning curves in airplane production, the age of the Dead Sea Scrolls, Apple and Oracle stock prices, the distance traveled by sports cars, lives saved by seat belts, and the cost of a congressional victory. The Seventh Edition maintains the hallmark features that have made BRIEF APPLIED CALCULUS so popular: contemporary and interesting applications including many that are new or updated); careful and effective use of technology, including graphing calculator and spreadsheet coverage; constant pedagogical reinforcement through section summaries, chapter summaries, annotated examples, and extra practice problems; Just-in-Time algebra review material; and a variety of exercises that allow readers to practice and hone their problem-solving skills.
TRACE and the arrow keys to check the values of your data points. When you are ﬁnished studying the data you have entered, press Yϭ ENTER to turn Plot1 off and then 2ND ϩ 4 ᭝ ENTER to clear all lists. xxiv Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not
1.17 1.14 2008 2009 2010 Year 72. BUSINESS: Biotechnology The S&P Index for the biotechnology subindustry is shown in the following graph. 128 S&P Index 130 120 121 117 112 110 100 2006 2007 2008 Year 2009 a. Number the years (bars) with x-values 1–4 and use linear regression to ﬁt a line to the data. State the regression formula. [Hint: See Example 8.] b. Interpret the slope of the line. c. Use the regression line to predict the S&P biotechnology index for the year 2020. 70.
Introduction In the previous section we learned how to differentiate the sum and difference of two functions — we simply take the sum or difference of the derivatives. In this section we learn how to differentiate the product and quotient of two functions. Unfortunately, we do not simply take the product or quotient of the derivatives. Matters are a little more complicated. Product Rule To differentiate the product of two functions, f(x) # g(x), we use the Product Rule. Product Rule d [ f(x) #
personal wealth. 86. True or False: To ﬁnd the rate of change of personal wealth, you would divide the rate of change of the national wealth by the rate of change of the population. Two Biomedical Applications 91. Beverton-Holt Recruitment Curve Some organisms exhibit a density-dependent mortality from one generation to the next. Let R . 1 be the net reproductive rate (that is, the number of surviving offspring per parent), let x . 0 be the density of parents, Copyright 2011 Cengage Learning.
product, where f and g are differentiable functions of x: d100 100 (x 2 4x99 1 3x50 1 6). dx100 d3 ( f # g) 5 f ‡ # g 1 3f – # g9 1 3f9 # g– 1 f # g ‡ dx 3 [Hint: You may use the “factorial” notation: n! 5 n(n 2 1) p 1. For example, 3! 5 3 # 2 # 1 5 6.] 2.6 [Hint: Use the Product Rule repeatedly.] [Hint: Differentiate the formula in Exercise 57 by the Product Rule.] The Chain Rule and the Generalized Power Rule Introduction In this section we will learn the last of the general rules of