Question

(a) Find the average value of the function f(x)=6(x−3)2 on the interval [2,5]. fave= 18/3 equation editorEquation Editor (b) Find two values of c such that fave=f(c). List these values in increasing order.

Answer 1

Answer:

$a) ~f_{avg} = 6\\b) ~c = 4,2$

Step-by-step explanation:

We are given the following in the question:

$f(x)=6(x-3)^2$

a) average value of the function on the interval [2,5]

$f_{avg} = \displaystyle\frac{f(5)-f(2)}{5-2}\\\\= \frac{6(5-3)^2 - 6(2-3)^2}{3}\\\\=\frac{24-6}{3} = \frac{18}{3} = 6\\\\f_{avg} = 6$

b) Value of c

$f_{avg} = f(c)\\6(c-3)^2 = 6\\(c-3)^2 = 1\\c-3 = \pm 1\\c-3 = 1, c-3 = -1\\c = 4, c =2$