Which of the following statements correctly describes the concavity of a…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Which of the following statements correctly describes the concavity of a differentiable function

f

on an interval? (a) If

f'(x)>0

for all

x

in the interval, then the graph of

f

is concave up on that interval. (b) If

f''(x)>0

for all

x

in the interval, then the graph of

f

is concave up on that interval. (c) If

f''(x)<0

for all

x

in the interval, then the graph of

f

is concave up on that interval. (d) If

f''(x)=0

for all

x

in the interval, then the graph of

f

is concave up on that interval.