266

4.8. (c)

Answers to Exercises and Solutions to Problems

~=~4-33~2+

=(x2-2)(x2-1)

J. X

Cd) J

\

i

\ \

\ \

\

y=x4-5x-6

/

x

‘\ \

\ \

\ \

\

(e) Y4

y=x4+5x-6

(0 Yt

J’ =x4 + 3x* ~ 36x

\ \

\

4.10. (a) Let p(x) = 6 x5 - 15x4 - 10x3 + 30x2 + 10. Then p'(x) = 30x4 -
60x3-30x2+60x = 30(2-2)(x- 1)2(x+ 1). p(z) is increasing for x 5 -1,
decreasing for -1 L x _< 0, increasing for 0 5 x 5 1, decreasing for
1 2 x < 2, increasing for 2 5 x. Also ~(-1) = 29 > 0, p(0) = 10 > 0,
p(1) = 21 > 0, p(2) = 2 > 0.

c-1,29)

7@

*

(1,211

4

(0, 10)

CL21

c