Section 5.2 – Applications of the Second Derivative.

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Presentation transcript:

Section 5.2 – Applications of the Second Derivative

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

+ _ + X X _ +

_ X 0 _ + _

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

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

_ X X

X CALCULATOR REQUIRED

NO CALCULATOR

X X X

CALCULATOR REQUIRED X X