Pre-Calc Homework Solutions 195

Pre-Calc Homework Solutions 195 - Chapter 4 Review 17. y...

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Unformatted text preview: Chapter 4 Review 17. y 6(x Intervals Sign of y Behavior of y Decreasing y 6(x 1)(2)(x 2) 6(x 2)[(2x 2) 18x(x 2) Intervals Sign of y Behavior of y Concave up Concave down Concave up (a) There are no local maxima. (b) There is a local (and absolute) minimum at x (c) There are points of inflection at x 18. y 6(x Intervals Sign of y Behavior of y Increasing y d 6(x 2 dx 195 1)(x 2)2 x 1 1 x 2 2 x 24. f (x) f (1) 3 4 1 3 1 2 3 4/3 x 4 1 3 x 3 1 2 x 2 x C 0 0 31 12 3 4/3 x 4 1 3 x 3 1 2 x 2 Increasing 2 Increasing 1 C C 6(x 2) (1) (x 2)] 0 x 2 2 x 25. v(t) s(t) s(0) C s(t) 26. a(t) v(t) v(0) C1 v(t) s(t) s(0) C2 s(t) 27. f (x) s (t) 4.9t 2 10 10 4.9t 2 f (x) 9.8t 5 5t C x 31 12 x 0 5t 10 1. 2. 0 and at x v (t) 32 32t C1 20 20 s (t) 16t 2 5 5 16t 2 tan x sec2 x f tan 1 2x 4 4 1)(x 2) x 1 1 x 2 2 x 32t 20t 20 C2 5 20t Decreasing 1) 1 2 Increasing x 2) x 6(2x 1 2 f (x) x L(x) Intervals Sign of y f 4 x 4 4 Behavior of y Concave down Concave up (a) There is a local maximum at x (b) There is a local minimum at x (c) There is a point of inflection at x d 19. Since dx 1 4 x 4 1 4 x 4 d sec x dx d 2 ln x dx sec 4 2 x 4 1. 2. 1 . 2 x 2x 2 1 28. f (x) f (x) L(x) sec x sec x tan x f 4 4 e e x x x C. 5 e , f (x) 20. Since 21. Since f (x) 22. Since f (x) 23. 1 f 4 x 4 4 sec x tan x, f (x) 1 3 x 3 1 3 x 3 sec x x2 1, C. sec 2 2x sec 2(1) x 2 4 tan 4 4 x 4 x x C. x 2 x 2 ln x 2 d 2 3/2 x 2x 1/2 dx 3 2 3/2 x 2x 1/2 C. 3 1 x , 29. f (x) f (x) 1 1 tan x (1 tan x) 2 (sec2 x) f (x) f( ) 0 C C f (x) cos x 3 3 2 cos x sin x C 1 cos2 x(1 tan x)2 1 (cos x sin x)2 sin x 2 L(x) f (0) 1 x f (0)(x 1(x 1 0) 0) ...
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