Left hand derivative of $f(x) = |x|$ at $x=0$ is

The correct answer is -1

Left hand derivative = $\lim\limits_{h\to 0^{-1}}$ $\dfrac{f(c+h) - f(c)}{h}$

In the above problem,

Left hand derivative = $\lim\limits_{x\to 0^{-1}}$ $\dfrac{f(x) - f(0)}{x-0}$ = $\lim\limits_{x\to 0^{-1}}$ $\dfrac{-x - 0}{x-0}$

= $\lim\limits_{x\to 0^{-1}} -1$ = $-1$