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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. 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. 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?