Answers to Math 151 WIR wk 11 5.2, 5.3, 5.5

1. a) critical values are -5, -1 and 3

b) local min at (-5, 0) and at (3, 0) local max at (-1, 4)

c) absolute max of 4 at x= -1, absolute min of 0 at x=3

d) absolute max of 40 at x=5, absolute min of 0 at x=3

2. g'(0)=0, g"(0)= -1 g has a local max at x=0.

3. local min of ln2+0.5 at x= -1, no local max., f has an inflection point at x = and

f is concave up on .

4. a) absolute min of -57 at x=-6, absolute max of 24 at x= -3

b) absolute min of -8 at x= 1, absolute max of 24 at x= -3

If f' has a local extremum at x=c the f has an inflection point at x=c.

5. a) c = 0.5 b) c = (a+b)/2

6. f has a local max of 1 at x=0, no local min. f has inflection points at .

7. local min at (3π/2, -3π/2 ) local max at ( π/2, π/2 ). f is decreasing on (π/2, 3π/2) and f is increasing on (0, π/2) and on (3π/2, 2π).

8. f'(x) = arctan x

f'(x) is negative for x<0 so f is decreasing for x<0. f'(x) is positive for x>0 so f is increasing for x>0

f has a local min at (0, 0). f'(x) is always increasing so f is always concave up.

9. no max or min at x=1 since f'(1) is not 0, no conclusion at x=2 ( 2nd derivative test fails),

local min at x=3, no max or min at x=4 since f'(4) is not 0, local max at x=5

10. local min at x=3, no local max. concave down on

concave up elsewhere.

11. radius = 2, height = 4

12.x = 3/2 and y = 2 for a maximum area of 3.