### Home > APCALC > Chapter 7 > Lesson 7.1.1 > Problem7-8

7-8.

For each function below, calculate the average value over the given interval and state the value of t such that g(t) equals the average value. Homework Help ✎

1. $g(t) = 3t + 6 \text{ for } [0, 8]$

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

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

1. $g(t) = 3e^t \text{ for } [0, 1]$

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

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?