Question

How does the first derivative test work?

Answer 1

First Derivative Test for Local Extrema
Let `x=c` be a critical value of `f(x)`.
If `f'(x)` changes its sign from + to - around `x=c`, then `f(c)` is a local maximum.
If `f'(x)` changes its sign from - to + around `x=c`, then `f(c)` is a local minimum.
If `f'(x)` does not change its sign around `x=c`, then `f(c)` is neither a local maximum nor a local minimum.