number 66,87

120 268 CHAPTER 3 Differentiation Rules 82. (a) Graph the function f(x) = x - 2 sin x in the viewing 65. At what points on the curve y = sin x + cos x, rectangle [0, 8] by [-2, 8]. 0 a, is used to model the concen- ( b) If P(xx) = f(x)g(x), find P'(2). tration at time t of a drug injected into the bloodstream. (c) If Q(x) = f(x) /g(x), find @'(1). (d) If C(x) = f(g(x)), find C'(2). (a) Show that lim,-. C(t) = 0. (b) Find C'(t), the rate of change of drug concentration in If f and g are the functions whose graphs are shown, let the blood. P ( x) = f ( x)g (x), e (x) = f(x)/g(x), and C(x) = f(g(x)). (c) When is this rate equal to O? Find (a) P'(2), (b ) Q'(2 ) , and (c ) C' ( 2 ) . 87. An equation of motion of the form s = Ae-"cos(wt + 8) represents damped oscillation of an object. Find the velocity and acceleration of the object. f 88. A particle moves along a horizontal line so that its coor- linate at time t is x = Vb2 + c2t2 , t > 0, where b and c Lea are positive constants. (a) Find the velocity and acceleration functions. (b) Show that the particle always moves in the positive 0 bait to-da direction. Find f' in terms of g'. 89. A particle moves on a vertical line so that its coordinate a ) = x2g(x) time t is y = 13 - 12t + 3, t = 0. 72. f(x) = g(x2) (a) Find the velocity and acceleration functions. = [g(x) 12 74. f(x) = g(g(x)) (b) When is the particle moving upward and when is it = g(ex ) 76. f(x) = es(x) moving downward? .SO (c) Find the distance that the particle travels in the time = In |g(x)| 78. f(x) = g(In x) interval 0 = t = 3. (d) Graph the position, velocity, and acceleration functi nd h' in terms of f' and g'. for 0