-2 l." lo

72

Part B 1.

C

-

Exam V Section I Calculators Permitted tl-

p.707

it_

f(x)=e'1r2

+11

1_ I 1. I

f'(x)=e''2x +1x2 +Dex = ex \x2 +2x+l) f"(x): r'12* +2) +(x2 +2x +l)ex : exlxz + 4x +3)= e*(x2 + 4x +3) :e'(x

+ 1)(x +

3)

{-3,-

!a_

1}

Thegraphof/haspointsofinflectionatx:-3andr:-1.(f"changesfrompositiveto negative at x:1, meaning that the graph changes from concave up to concave down; at x : -Lt the concavity switches back again.) Thus, there are 2 points of inflection. The answer is C.

,.1 1_ 1 L z !a_

1 L Z L I !4.

2.

C

1_ ,1

{-

p.107 10

:/soo"-'zL dt

Volume

:

I -.zt'l 1o -2 l." lo soo

,a 114

2161.7

1-1 !_ t

J.

B

p. 108

!4._

Given the sales function S(t), the rate of change of sales is given by S'(t) : -.46 (.45) sin(.45t + 3.15) . The derivative of S'is S"(t) : -.46 (.45)(,45) cos(.4st + 3.15) .

ra_

4 !L I I L

calculator, you find that the function S" has one zero on the interval [O 10] at t:3.4719. Since S"(t) > 0 for 0 0 1.-*112 ,o *112 .1 0<x