Suppose the graph of has a local minimum at and is differentiable there

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Suppose the graph of k′(x)k'(x) has a local minimum at x=4x=4 and is differentiable there. Which statement about k′′(4)k''(4) must be true? (a) k′′(4)>0k''(4)>0 (b) k′′(4)=0k''(4)=0 (c) k′′(4)k''(4) does not exist (d) k′′(4)<0k''(4)<0

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