FILL IN THE BLANK!!!!!! Find the absolute maximum and minimum values of the func

Question

FILL IN THE BLANK!!!!!!

Find the absolute maximum and minimum values of the function below.

f(x)= 2x^3 - 30x^2 + 3      -5/2 (less than or equal to) x (less than or equal to) 20

Since f is continuous on [____, _____] we can use the Closed Interval Method:

f(x)= 2x^3 - 30x^2 + 3

f' (x)= _______

Since f '(x) exists for all x, the only critical numbers of f occur when f '(x) = _______  that is, x = 0

or x = ______. Notice that each of these critical numbers lies in the domain of f(x). The values of f at these critical numbers are f(0) = ______, and f(10) = _______

The values of f at the endpoints of the interval are f(-5/2) = ______ and f(20) = ______

Comparing these four numbers, we see that the absolute maximum value is f(20) = _____, and the absolute minimum value is f(10) = _____

Explanation / Answer

FILL IN THE BLANK!!!!!!

Find the absolute maximum and minimum values of the function below.

f(x)= 2x^3 - 30x^2 + 3 -5/2 (less than or equal to) x (less than or equal to) 20

Since f is continuous on [_-5/2___, ___20__] we can use the Closed Interval Method:

f(x)= 2x^3 - 30x^2 + 3

f' (x)= __6x^2 - 60x_____

Since f '(x) exists for all x, the only critical numbers of f occur when f '(x) = ___0____ that is, x = 0

or x = ___10___. Notice that each of these critical numbers lies in the domain of f(x). The values of f at these critical numbers are f(0) = __3____, and f(10) = __-997_____

The values of f at the endpoints of the interval are f(-5/2) = __-215.75____ and f(20) = __4003____

Comparing these four numbers, we see that the absolute maximum value is f(20) = __4003___, and the absolute minimum value is f(10) = __-997___

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