Mathematics

Mathematics

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

.

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