A test for monotonicity: Using the derivative to understand the monotonicity of a function

When the sign of f'(x) is positive (respectively, negative) throughout an open interval, then the function is strictly increasing (respectively, negative) on that open interval. This theorem is an important consequence of the Mean Value Theorem, and it can be generalized to include weak monotonicity and the conclusion can be applied to closed intervals when the original function is continuous at the endpoints.

Видео A test for monotonicity: Using the derivative to understand the monotonicity of a function канала Chris Odden