Which of the following conditions on a differentiable function at guarantees that is…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Which of the following conditions on a differentiable function ff at x=cx=c guarantees that f(c)f(c) is a local minimum? (a) f′(c)=0 and f′′(c)<0f'(c)=0\text{ and }f''(c)<0 (b) f′(c)=0 and f′′(c)=0f'(c)=0\text{ and }f''(c)=0 (c) f′(c)=0 and f′′(c)>0f'(c)=0\text{ and }f''(c)>0 (d) f′(c)>0 and f′′(c)=0f'(c)>0\text{ and }f''(c)=0

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