Which of the following correctly relates the sign of to the concavity of a…

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

Problem

Which of the following correctly relates the sign of

f''(x)

to the concavity of a twice-differentiable function

f

on an interval

I

? (a) If

f''(x)>0

for all

x\in I

, then

f

is concave down on

I

. (b) If

f''(x)>0

for all

x\in I

, then

f

is increasing on

I

. (c) If

f''(x)>0

for all

x\in I

, then

f

is concave up on

I

. (d) If

f''(x)<0

for all

x\in I

, then

f

is concave up on

I