I'm taking calculus one and I have to determine if this statement is true or false.
A relative maximum or minimum must occur at a critical point.
I believe it is false. The answer key says it is true so I am curious if I am right (low probability) or if I can get this clarified (the answer key has always been right when I thought it was wrong).
For example for y = $\frac{1}{x}$ there is a critical point at x=0 (because the derivative at this point does not exist) even though there is no relative maximum or minimum (or is there?).
I think if the statement was "A relative maximum or minimum must occur at a critical point when the derivative at that point exists."
Please help. Thanks.