Going Further

The Intermediate Value Theorem (from 141) tells us that there must be (at least) one point in the interval 0 <= <= 4 where the function f attains its average value on the interval. That is, where . First, convince yourself that this is true in this example by graphing the function and the average value in the same plot. Use this plot to estimate the point where . Next, find the exact value of w where this intersection occurs.

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Solution