FILL IN THE BLANK Find the absolute maximum and minimum valu

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) = _____

Solution

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___