A twice-differentiable function satisfies

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

Problem

A twice-differentiable function gg satisfies g(−2)=g(2)g(-2)=g(2). Which of the following conclusions must be true? (a) There exists a number cc in (−2,2)(-2,2) such that g′′(c)=0g''(c)=0. (b) There exists a number cc in (−2,2)(-2,2) such that g(c)=0g(c)=0. (c) There exists a number cc in (−2,2)(-2,2) such that g′(c)=0g'(c)=0. (d) g′(0)=0g'(0)=0.

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