1. Section 5.2 – Applications of the Second Derivative

2. THE SECOND DERIVATIVE TEST FOR MAX/MIN Theory First…. POINT OF INFLECTION TEST FOR CONCAVITY

3. + _ + X X _ +

4. 0 1 + + _ X 0 _ + _

5. Since f ‘ (-2) = 0 and f “ (-2) < 0 there is a relative max at x = -2, but x = -2 is not on the interval [0, 2] Since f(2) > f(0), the abs max occurs at x = 2 The maximum value is 8

6. 2 4 7 + _ ++ x = 2 since f “ (x) changes from pos to neg. x = 4 since f “ (x) changes from neg to pos.

7. 1 4 + + _ X X

8. X CALCULATOR REQUIRED

11. NO CALCULATOR

12. X X X

18. CALCULATOR REQUIRED X X