1. Section 4.1 Maxima and Minima 1

2. 2

3. 3

4. 4 a.Satisfies the conditions of the Extreme Value Theorem. Absolute maximum at x = a and absolute minimum at x = c. Absolute maximum at x = c

5. 5

6. 6 Absolute maximum: q and s Local maximum: q and s Absolute minimum: p Local minimum: p and r If f has a local maximum or minimum at c and f’(c) exists, then f’(c) = 0.

7. 7 Note the converse of Theorem is not necessarily true.

8. 8 X(2ln x + 1) = 0; x = 0 not in domain or 2ln x + 1 = 0 ln x = -1/2 x = e -1/2 ≈ 0.61

9. 9

10. 10 f(-2) = 32 absolute maximum f(3/2) = -27/16 absolute minimum a.

11. 11 b. g(-1) = 3 absolute maximum and g(0) = g(2) = 0 absolute minimum

12. 12 SOLUTION