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Section 5.2 – Applications of the Second Derivative.

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Presentation on theme: "Section 5.2 – Applications of the Second Derivative."— Presentation transcript:

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

9

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11 NO CALCULATOR

12 X X X

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18 CALCULATOR REQUIRED X X


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