Which of the following statements is true for a differentiable function defined on an…

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

Problem

Which of the following statements is true for a differentiable function

f

defined on an open interval

I

? (a) If

f'(x)=0

at some

c\in I

, then

f

must have a relative extremum at

c

. (b) If

f'(x)

does not change sign on

I

, then

f

must be constant on

I

. (c) If

f'(x)>0

for every

x

I

, then

f

is increasing on

I

. (d) If

f'(x)>0

for some

x

I

, then

f

is increasing on

I