Answer
-0.00222
Work Step by Step
Given/Known: $ f(x)=x^{-1}$, $ a=3$, $\Delta x=0.02$ and $ f'(x)=-\frac{1}{x^{2}}$
Recall: $ f(a+\Delta x)-f(a)=f'(a)\Delta x $
$\implies $ $ f(3+0.02)-f(3)=f'(3)\times\Delta x=-\frac{1}{3^{2}}\times0.02$
$=-0.00222$