Find the absolute extrema of the function on the closed interval Round your answer to two decimal places.
A) The maximum of the function is 1 and the minimum of the function is 0.
B) The maximum of the function is 2.92 and the minimum of the function is 1.
C) The maximum of the function is 2.92 and the minimum of the function is 0.
D) The maximum of the function is1 and the minimum of the function is 2.52.
E) The maximum of the function is 0 and the minimum of the function is 2.52.

Question

​Find the absolute extrema of the function  on the closed interval  Round your answer to two decimal places. ​
A) ​The maximum of the function is 1 and the minimum of the function is 0. 
B) ​The maximum of the function is 2.92 and the minimum of the function is 1. 
C) ​The maximum of the function is 2.92 and the minimum of the function is 0. 
D) ​The maximum of the function is1 and the minimum of the function is 2.52. 
E) ​The maximum of the function is 0 and the minimum of the function is 2.52.

Quizplus · Accepted Answer

To find the absolute extrema of the function, we need to consider both the critical points and the endpoints of the interval.

Taking the derivative of the function, we get:

f'(x) = 11x^10 - 22x^9

Setting f'(x) = 0, we get:

11x^9 (x - 2) = 0

This gives us two critical points: x = 0 and x = 2.

Next, we evaluate f(x) at the critical points and the endpoints of the interval:

f(0) = 0 
f(1) = 2 
f(2) = 0

Therefore, the maximum of the function is 2 (at x = 1) and the minimum of the function is 0 (at x = 0 and x = 2). Rounding to two decimal places, we get the answer as C.

​Find the Absolute Extrema of the Function on the Closed

Find the Absolute Extrema of the Function on the Closed