Classifying Critical Points and Extreme Values for a Function
Key Questions

Here is how to find and classify a critical point of
#f# .Remember that
#x=c# is called a critical value of#f# if#f'(c)=0# or#f'(c)# is undefined.#f'(x)=3x^2=0 Rightarrow x=0# is a critical number.(Note:
#f'# is defined everywhere,#0# is the only critical value.)Observing that
#f'(x)=3x^2 ge 0# for all#x# ,#f'# does not change sign around the critical value#0# .Hence,
#f(0)# is neither a local maximum nor a local minimum by First Derivative Test.
Questions
Graphing with the First Derivative

Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)

Identifying Stationary Points (Critical Points) for a Function

Identifying Turning Points (Local Extrema) for a Function

Classifying Critical Points and Extreme Values for a Function

Mean Value Theorem for Continuous Functions