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

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 ✎

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?