Consider the given function and the given interval.

Question

f(x) = (x − 3)^2, [2, 5]

(a) Find the average value fave of f on the given interval.
fave =

(b) Find c such that fave = f(c).
c = (smaller value)
c= (larger value)

Answer 1

recall that the average value of f(x) on [a,b] is

(∫[a,b] f(x) dx)/(b-a)

now just plug and chug.