Question

Find the absolute maximum value of f(x)=2x³+3x²-12 on the interval [0,2].

Answer 1

To find the absolute maximum value of the function on the given interval, we can follow the steps of finding critical points, evaluating the function at these points, and comparing the values.

Step-by-step explanation:

To find the absolute maximum value of the function f(x)=2x³+3x²-12 on the interval [0,2], we can follow these steps:

1. Find the critical points by taking the derivative of the function and setting it equal to zero.
2. Evaluate the function at the critical points and the endpoints of the interval.
3. Compare the values to determine the absolute maximum value.

In this case, the critical point is x=0 and the function evaluated at x=0 is f(0)=-12. The function evaluated at x=2 is f(2)=20. Since f(2) is greater than f(0) and there are no other critical points or endpoints within the interval, the absolute maximum value of f(x) on the interval [0,2] is 20.