Question

Find whether the function $f(x) = \begin{cases} x - 1, & x < 2 \\ 2x - 3, & x \ge 2 \end{cases}$ at $x = 2$ is differentiable or not.

Hint:

For simple piecewise linear functions, you can find the derivatives of the individual branches directly. The derivative of the left branch ($x-1$) is 1, and the derivative of the right branch ($2x-3$) is 2. Since $1 \neq 2$, it is instantly proven non-differentiable!

Answer 1