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Show that the function is continuous at but not differentiable.
Show that the function $f(x) = \begin{cases} x^2, & x \le 1 \\ \frac{1}{x}, & x > 1 \end{cases}$ is continuous at $x = 1$ but not differentiable.
Given: $f(x) = \begin{cases} x^2, & x \le 1 \\ \frac{1}{x}, & x > 1 \end{cases}$
To show: $f(x)$ is continuous at $x = 1$ but not differentiable
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From ISC 2018 Mathematics Paper 1, question 5(a).