Question: If f ( x ) = 1 x n , then f ' ( x ) = 1 n x n - 1 . Finding

f (x) = \frac{1}{x^{n}},

then

f^{'} (x) = \frac{1}{n x^{n - 1}} .

Finding Rates of Change In Excrises

99, 100, 101, 102, 103,

and

104

find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.

99 . f (t) = 3 t 5, [1, 2]

If f ( x ) = 1 x n , then f ' ( x ) = 1 n x n - 1

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