Let and be twice-differentiable functions on such that for all in

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

Problem

Let

p

and

q

be twice-differentiable functions on

(0,4)

such that

p''(x)<q''(x)

for all

x

(0,4)

. Which of the following best compares the concavity of the graphs of

p

and

q

(0,4)

? (a) The graph of

p

is more concave up than the graph of

q

(0,4)

. (b) The graph of

q

is more concave up than the graph of

p

(0,4)

. (c) Both graphs have identical concavity on

(0,4)

. (d) Both graphs are concave up on

(0,4)