# How do you find the average rate of change of #f(x)= -1/x# from [1,2]?

In this instance

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To find the average rate of change of ( f(x) = -\frac{1}{x} ) from ( x = 1 ) to ( x = 2 ), use the formula:

[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} ]

where ( a = 1 ) and ( b = 2 ).

[ f(1) = -1/1 = -1 ] [ f(2) = -1/2 ]

Plug these values into the formula:

[ \text{Average Rate of Change} = \frac{f(2) - f(1)}{2 - 1} ] [ = \frac{-1/2 - (-1)}{1} ] [ = \frac{-1/2 + 1}{1} ] [ = \frac{1 - 1/2}{1} ] [ = \frac{1/2}{1} ] [ = \frac{1}{2} ]

So, the average rate of change of ( f(x) = -\frac{1}{x} ) from ( x = 1 ) to ( x = 2 ) is ( \frac{1}{2} ).

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