Question

Find the extreme values of the function f on the interval [0,π], and the x-value(s) at which they occur. If an extreme value does not exist, enter DNE for both the value

Answer 1

To find the extreme values of the function f on the interval [0,π], you need to take the derivative of the function and find the critical points. The highest and lowest values of the function at the critical points and the endpoints of the interval will be the extreme values. If there are no critical points, the extreme values do not exist.

Step-by-step explanation:

To find the extreme values of the function f on the interval [0,π], we need to take the derivative of the function and find the critical points. Let's assume the function is given by f(x). The critical points occur where the derivative is either zero or undefined.

1. Take the derivative of f(x) with respect to x.
2. Equate the derivative to zero and solve for x. These are the potential critical points.
3. Check the value of f(x) at the critical points and at the endpoints of the interval [0,π]. The highest and lowest values will be the extreme values.
4. If there are no critical points, then label the extreme values as DNE (Does Not Exist).
5. Record the x-values at which the extreme values occur.

By following these steps, you will be able to find the extreme values of the function f on the interval [0,π] and identify the x-values at which they occur.