A differentiable function satisfies the following: increases on and decreases on

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

Problem

A differentiable function

g

satisfies the following:

g

increases on

(1,4)

and decreases on

(4,7)

. Let

f

be defined by

f(x)=g'(x)

. Which statement about

f

is most accurate? (a)

f(x)<0

for

1<x<4

and

f(x)>0

for

4<x<7

(b)

f(x)<0

for both

1<x<4

and

4<x<7

(c)

f(x)>0

for

1<x<4

and

f(x)<0

for

4<x<7

(d)

f(x)>0

for both

1<x<4

and

4<x<7