MAXIMUM AND MINIMUM VALUES OF A FUNCTION

To find the maximum and minimum values of a function, you typically follow these steps:

1. Find the critical points by setting the derivative of the function equal to zero and solving for x.
2. Evaluate the function at these critical points and at the endpoints of the interval of interest.
3. Compare the values obtained in step 2 to determine the maximum and minimum values.

Here’s a more detailed explanation:

1. Find the critical points: Given a function f(x), find f′(x) and set it equal to zero to find critical points.
2. Determine the endpoints of the interval of interest, if any.
3. Evaluate the function at the critical points and the endpoints of the interval of interest.
4. The largest and smallest values obtained in step 3 will be the maximum and minimum values of the function, respectively