Science:Math Exam Resources/Courses/MATH100 A/December 2024/Question 14/Statement

Let $f(x)$ be a function that is defined for all real numbers by

$$f(x)=\{\begin{array}{ll}{x}^2& \text{if }x=\frac{1}{n},\text{where}n\text{is a positive integer}\\ 0& \text{otherwise.}\\ \end{array}$$

A portion of the function is sketched below, to help you visualize it.

For what values of x is this function differentiable? For those values, compute $f^{\prime }(x)$. Remember to fully justify your answer.