Answer
$f'(1) = -1$
$f'(2) = -\frac{1}{4}$
$f'(3) = -\frac{1}{9}$
Work Step by Step
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:
$f'(1) = -(1)^{-2} = -1$
$f'(2) = -(2)^{-2} = -\frac{1}{4}$
$f'(3) = -(3)^{-2} = -\frac{1}{9}$
