find local minimum and local maximum at (0,4)

YOu forgot to post your answer and what you did to get it...

Or at least how you think you should find the answer...

We don't do your homework assignments so you don't have to try.

The question as posed makes no sense, as the point (0,4) is not on the function that you wrote. Or perhaps you meant to find the local min and local max in the domain 0<=x<=4? It would help to know what level of mathematics you are taking - are you learning about graphing functions in high school, or is this for a course in calculus?