An even function is twice differentiable for all real numbers and satisfies along with for
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
An even function h is twice differentiable for all real numbers and satisfies h(−4)=h(4)=7 along with h′′(x)>0 for −4<x<4. Which statement is necessarily true?
(a) h has exactly two stationary points in (−4,4), located symmetrically about 0, both of which are local minima.
(b) h has exactly one stationary point in (−4,4), located at x=0, and this point is a local maximum.
(c) h has exactly one stationary point in (−4,4), located at x=0, and this point is a local minimum.
(d) h must have at least one stationary point in (−4,4), but the number and nature of such points cannot be determined from the given information.