Suppose a differentiable function satisfies and for all in an open interval

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Suppose a differentiable function

f

satisfies

f'(x)>0

and

f''(x)<0

for all

x

in an open interval

(a,b)

. Which of the following best describes the graph of

f

(a,b)

? (a) Increasing and concave up (b) Decreasing and concave up (c) Increasing and concave down (d) Decreasing and concave down