Critical numbers

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

Types of Problems
There are four types of problems in this exercise. 1. 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.

2. 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.

3. 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.

4. 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.

5. Find the critical numbers of the function: The student is asked to find the critical numbers by using the function given.

Strategies
Knowledge of the first derivative and critical number concepts are encouraged to ensure success on this exercise. 1. 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 g′(c)=0 or g′(c)  is undefined."

2. Critical points cannot be endpoints.

3. If the first derivative goes from negative to positive, it is a minimum.

4. If the first derivative goes from positive to negative, it is a maximum.

5. A global minimum is the minimum that has the lowest y-value of the original function.

6. A global maximum is the maximum that has the highest y-value of the original function.