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.