Consider the given function and the given interval. f(x) = (x − 4)2, [3, 6]
(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)

f average = 1

smaller value c = 3

larger value c = 5

Step-by-step explanation:

Functions can be represented using equations.

The function is given as:

(a) The average value

This is calculated as:

So, we have:

Calculate f(6) and f(3)

So, we have:

Hence, the average value of the function is 1

Substitute c for x in:

So, we have:

Take square roots of both sides

Add 4 to both sides

Split

Hence, the smaller and larger values of c are: 3 and 5

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