Let be a differentiable function whose derivative satisfies for ,

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

Problem

Let

f

be a differentiable function whose derivative satisfies

f'(x)>0

for

-3<x<1

f'(1)=0

, and

f'(x)<0

for

1<x<4

. Determine the nature of the critical point of

f

x=1

(relative minimum, relative maximum, or neither).