Question

Locate the absolute extrema of the function on the closed interval calculator?

a) At critical points
b) At endpoints
c) At stationary points
d) At inflection points

Answer 1

To locate the absolute extrema of a function on a closed interval, find the critical points and evaluate the function at the critical points and endpoints.

Step-by-step explanation:

To locate the absolute extrema of a function on a closed interval, follow these steps:

1. Determine the critical points of the function by finding the values of x where the derivative equals zero or is undefined.
2. Evaluate the function at the critical points and the endpoints of the interval.
3. The highest and lowest values from step 2 are the absolute maximum and minimum, respectively.

For example, if the function is f(x) = x^2 on the interval [-1, 2], the critical point is x = 0. Evaluating the function at the critical point and the endpoints, we get f(-1) = 1, f(0) = 0, and f(2) = 4. The absolute maximum is 4 at x = 2, and the absolute minimum is 0 at x = 0.