### Home > CALC > Chapter 7 > Lesson 7.1.1 > Problem 7-8

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. Homework Help ✎*g*(*t*) = 3*t*+ 6 for [0, 8]*g*(*t*) = 3*e*for [0, 1]^{t}

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*.

Average Value = 3*e* − 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?