Question

what does NO relative extrema mean? if my critical value is a 0, is there an extrema?

Answer 1

An example is a situation like this. You see that at x=0, f'(x)=0 but that is neither a relative maximum or minimum of the graph.
Relative is used here to mean the same thing as local. In the small area around x=0, the function does not have an extremum

Answer 2

so no extrema? I know how to solve it and sketch graph, I just don't know if there's an extrema.

Answer 3

thank you. btw, you are very smart :)

Answer 4

There are various methods to test whether a critical point is an extrema. You can use the second derivative to check for concavity. Or you can check how the derivative behaves around your critical point.

For example. If f is decreasing before the critical point, and is increasing after, then you have a local minimum. This check is done within an interval not containing any other critical points

Answer 5

thanks. I did that.