CPM Homework Help : CALC Problem 7-8

For each function below, find its average value on the given integral and state the time $t$ at which it equals its average value.

$g(t) = 3t + 6$ for [ $0, 8$ ]

$g(t) = 3e^t$ for [ $0, 1$ ]

Hint 1(a):

Read the Math Note about how to compute the Mean Value of $g(x)$ , given $g(x)$ .

Hint 2(a):

To find the the time the function is at its average value, let $g(t) =$ the average value and solve for $t$ .

Partial Answer (b):

Average Value $= 3e − 3$ . Now find the time, $t$ , that $g(t) =$ its average value.

Hint (b):

The Mean Value Theorem states that a differentiable function will reach its average (mean) value at least once on any closed interval.
Check your values of $t$ in parts (a) and (b). Are they within the the given closed intervals?