The **Critical Numbers** exercise appears under the Differential calculus Math Mission on Khan Academy. This exercise uses the first derivative test to find minimums and maximums of the original function.

## Types of Problems Edit

There are five types of problems in this exercise:

*Find the local minimums/maximums using a graph of the first derivative:*The student is asked to find the local minimums and maximums given the graph of the first derivative.*Find the critical numbers using a graph of the original function:*The student is asked to find all the critical points by using the graph of the original function.*Find the values given a table of the original function and its derivative:*The student is asked to find the values of the critical numbers, minimums, and maximums using a table of the original function and its derivative.*Find the amount of critical numbers there are given a graph of the original function:*The student is asked to find how many critical numbers there are by using the graph provided.*Find the critical numbers of the function:*The student is asked to find the critical numbers by using the function given.

## Strategies Edit

Knowledge of the first derivative and critical number concepts are encouraged to ensure success on this exercise.

- Critical number: "The number c is a critical number of a function g if and only if c is in the domain of g and either or is undefined."
- Critical points cannot be endpoints.
- If the first derivative goes from negative to positive, it is a minimum.
- If the first derivative goes from positive to negative, it is a maximum.
- A global minimum is the minimum that has the lowest y-value of the original function.
- A global maximum is the maximum that has the highest y-value of the original function.

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