For a differentiable function

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

f

, it is known that •

f'(x)>0

for

x<0

•

f'(x)<0

for

0<x<2

•

f'(2)=0

•

f'(x)>0

for

x>2

and that

f(0)=3

and

f(2)=1

. (a) State the intervals on which

f

is increasing and the intervals on which it is decreasing. (b) Draw a rough sketch of the graph of

y=f(x)

, marking the points

(0,3)

and

(2,1)