Question

Using calculus, find the absolute maximum and absolute minimum of the function f(x)=6x²−36x 1 on the interval [−5,5].

A) Max at x = 5, Min at x = -5
B) Max at x = -3, Min at x = 3
C) Max at x = -5, Min at x = 5
D) Max at x = 3, Min at x = -3

Answer 1

To find the absolute maximum and absolute minimum of the function f(x) = 6x² - 36x on the interval [-5,5], follow these steps:

Step-by-step explanation:

To find the absolute maximum and absolute minimum of the function f(x) = 6x² - 36x on the interval [-5,5], we can follow these steps:

1. Find the critical points of the function by setting the derivative equal to zero and solving for x.
2. Check if the critical points lie within the interval [-5,5], and if so, evaluate the function at those points.
3. Find the function values at the endpoints of the interval, which are -5 and 5.
4. Compare all the values obtained in steps 2 and 3 to determine the absolute maximum and absolute minimum.

By following these steps, we can determine that the absolute maximum occurs at x = 5 and the absolute minimum occurs at x = -5.