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

  1. for []

  1. for []

Read the Math Note about how to compute the Mean Value of , given .

To find the the time the function is at its average value, let the average value and solve for .

Average Value . Now find the time, , that 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 in parts (a) and (b). Are they within the the given closed intervals?