identify the increasing/decreasing or maximum/minimum

[calmandy]

Use the graph of f'(x) to identify the intervals on which is f(x) is increasing or decreasing and estimate the values of x on which f(x) has relative maximum or minimum. Explain.

This is the picture of f'(x)

This is my answer: Local max: x= 1
Local min x=3
Increasing on [5/2 , positive infinity)
Decreasing on ( negative infinity, 5/2]

Guys, help me check my answer please
thank you

 

[DrMike]

This is my answer: Local max: x= 1

Correct..

Local min x=3

Looks good to me...

Increasing on [5/2 , positive infinity)

No. f(x) is increasing if f'(x) is positive.

Decreasing on ( negative infinity, 5/2]

No. f(x) is decreasing if f'(x) is negative.