Find the absolute extrema of the given function on the indicated interval. on

Question

Find the absolute extrema of the given function on the indicated interval.  on

Quizplus · Accepted Answer

To find the absolute extrema, we take the derivative of the given function and set it equal to zero. We get:

f'(x) = 3x^2 - 12x + 9 = 3(x-1)^2

Setting f'(x) = 0, we find that the critical point is x=1.

Next, we check the values of the function at the critical point and the endpoints of the interval. We get:

f(0) = 9, f(1) = 6, f(2) = 9/4

Therefore, the absolute maximum is f(0) = 9 and the absolute minimum is f(1) = 6.

Choice C matches these values, so it is the correct answer.

Find the Absolute Extrema of the Given Function on the Indicated