First Derivative Sign Test

First Derivative Sign Test

If $$f'(x)$$ changes from positive to negative at $$x=c$$:

$$+\rightarrow-$$

then $$f(c)$$ is a local maximum.

If $$f'(x)$$ changes from negative to positive:

$$-\rightarrow+$$

then $$f(c)$$ is a local minimum.

Usage

- Used to classify critical points without calculating higher derivatives.