## Calculus (3rd Edition)

$f'(1) = -1$ $f'(2) = -\frac{1}{4}$ $f'(3) = -\frac{1}{9}$
Let $f(x) = \frac{1}{x}$ To find the rate of change, we need to find the derivative of the function, which we can do using the power rule: $f(x) = x^{-1}$ $f'(x) = -x^{-2}$ Now, to find the rate at each point, we substitute x for each point given: $f'(1) = -(1)^{-2} = -1$ $f'(2) = -(2)^{-2} = -\frac{1}{4}$ $f'(3) = -(3)^{-2} = -\frac{1}{9}$