Science:Math Exam Resources/Courses/MATH110/April 2016/Question 08 (c)/Solution 1

You should start by drawing a graph of $\frac{1}{x}$. We take the tangent line at the point $(4,\frac{1}{4})$. We compare the point $A=(4.16,\frac{1}{4.16})$ on the graph of $y=\frac{1}{x}$ and the point $B=(4.16,0.24)$ on the graph of the tangent line. The linear approximation at point $B$ is seen to be an underestimate.