Find the absolute extrema of the function on the interval
A) The maximum of the function is 1 and the minimum of the function is 0..
B) The maximum of the function is 0 and the minimum of the function is -1..
C) The maximum of the function is -1 and the minimum of the function is 0.
D) The maximum of the function is 1 and the minimum of the function is 0.
E) The maximum of the function is 0 and the minimum of the function is 1.

Question

​Find the absolute extrema of the function  on the interval  ​
A) ​The maximum of the function is 1 and the minimum of the function is 0.. 
B) ​The maximum of the function is 0 and the minimum of the function is -1.. 
C) ​The maximum of the function is -1 and the minimum of the function is 0. 
D) ​The maximum of the function is 1 and the minimum of the function is 0. 
E) ​The maximum of the function is 0 and the minimum of the function is 1.

Quizplus · Accepted Answer

To find the absolute extrema, we need to find the critical points on the given interval and evaluate the function at those points and the endpoints of the interval. 
Taking the derivative of the function, we get:
f'(x) = 3x^2 - 6x
Setting this equal to 0, we get:
3x(x-2) = 0
Thus, the critical points are x=0 and x=2. 
Evaluating the function at these points, we get:
f(0) = 0 and f(2) = 1
Also, evaluating the function at the endpoints of the interval, we get:
f(-1) = 1 and f(3) = 0
Therefore, the absolute maximum is f(-1) = 1 and the absolute minimum is f(3) = 0. 
Thus, the correct answer is D: The maximum of the function is 1 and the minimum of the function is 0.

​Find the Absolute Extrema of the Function on the Interval

Find the Absolute Extrema of the Function on the Interval