Science:Math Exam Resources/Courses/MATH110/April 2018/Question 08 (d)/Solution 1

The function ${\textstyle y=e^{x}}$ is convex so the linear approximation will give an underestimate, whereas the function ${\textstyle y={\sqrt {x}}}$ is concave so the linear approximation will give an overestimate. This is shown in the following sketches of the functions with their respective linear approximations.

Answer: The approximation using ${\textstyle {\color {blue}f(x)=e^{x}}}$ will be an underestimate.