Question

vTo find the absolute minimum and maximum values of the function f(x) = x⁴ - 18x² + 8, we need to find the local minimum and maximum values within the range -2 <= x <= 7 and compare them to the function values at the endpoints of the range.

Answer 1

To find the absolute minimum and maximum values of the function f(x) = x⁴ - 18x² + 8, follow these steps: Find the critical points, identify any points of discontinuity, evaluate the function at critical points and endpoints, and compare the results.

Step-by-step explanation:

To find the absolute minimum and maximum values of the function f(x) = x⁴ - 18x² + 8, we need to follow these steps:

1. Find the critical points of the function by setting the derivative equal to zero and solving for x.
2. Identify any points of discontinuity within the given range.
3. Evaluate the function at the critical points and endpoints of the range.
4. Compare the function values to determine the absolute minimum and maximum.

In this case, the critical points can be found by solving for x when f'(x) = 0. Then, evaluate the function at these critical points and the endpoints of the given range.