Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 172: 3

-0.00222

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$ $=-0.00222$