A twice differentiable function satisfies and

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A twice differentiable function

f

satisfies

f(4)=3

and

f'(4)=2

. Its second derivative is negative on the interval

(4,7)

. The linear approximation to

f

x=4

L(x)=3+2(x-4)

. At

x=5

, does

L(5)

overestimate or underestimate the actual value of

f(5)

? Explain using concavity.