# 188Chapter 3Applications of Differentiation71. Anaf haFindingTechnology In Exercises 49-54, (a) use a computer algebraan to diferentiate the function, (b) sketch the graphs of2 3PEA om the same set of coordinate axes over the givenSma (c) find the critical numbers of f in the open interval,18 Gad chhe h.terval(s) on which f' is positive and the)or which f'is negative. Compare the behavior of fca he ign offUsingandAnalyzingDerivativesEXPLORING CONCEPTSTransformations of Functions In Exercises 63-66,assume that f is differentiable for all x. The signs of fexinare as follows.72. Anf'(x) > 0 on (-0, -4)f'(x) < 0 on (-4, 6)f'(x)> 0 on (6, oo)48 FO) = 2x/9- x, [-3, 3]0 /) = 10(5 - 3x+ 16),ThinkdifferSupply the appropriate inequality sign for the indicated[0, 5]value of c.SL f(D =2 sin t, [0, 2]seleSign of g'(c)Function52. f)=2-+cos [0, 47]the+COSg'(0)1063. g(x) f(x) +573.fisg'(-5)53. f(x) 3 sin064. g(x) 3f(x) - 3[0, 67]g'(-6)065. g(x)f(x)54. f(x) 2 sin 3x + 4 cos 3x, [0, 7T]'(0)066. g(x) = f(x - 10)Comparing FunctionsIn Exercises 55 and 56, usesymmetry, extrema, and zeros to sketch the graph of f. Howdo the functions f and g differ?Sketch the graph of the arbitrary67. Sketchinga Graphfunction f such that-4x3 3x0,x < 455. f(x) =f'(x){undefined,x2- 1x = 4.74. f 4g(x) = x(x2 - 3)56. f(t) cos2t- sin2 tIs the sum of two increasing68. Increasing Functionsfunctions always increasing? Explain.11 - 2 sin2 tg(t)69. Increasing Functions Is the product of twoincreasing functions always increasing? Explain.Think About It In Exercises 57-62, the graph of f is shownin the figure. Sketch a graph of the derivative of f. To print anenlarged copy of the graph, go to MathGraphs.com57.y58.y. HOW DO YOU SEE IT? Use the graph off' to (a) identify the critical numbers of f(b) identify the open intervals on which f isincreasing or decreasing, and (c) determinewhether f has a relative maximum, a relativeminimum, or neither at each critical number.75.42ff1++2 --2 -112 31++-2 -1+1 2(i)59.y60.(ii)f'2.f624-224+-4-22-2-6 8A 76.-6-4-4+4 6-4-6+2-4-2-2+61.62.y(ii)6-(iv)422 4-4 -22 4-22 462 4-2 +-6-4-2-6+4t22

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Step 1

To sketch the graph of the derivative of f(x) , given the graph of f(x)

Step 2

The graph of y=f(x) is a straight line , with (constant) slope 2. so the derivat...

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