What is the derivative of f(x) = $| x |$ at x = 0?

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-1

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Does not exist

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Solution

The correct option is D Does not exist
f(x) = $| x |$ = ${\begin{matrix} x, x > 0 - x, x < 0 \end{matrix}$

Left derivative = -1

Right derivative = +1

$∵ L D \neq R D$

The derivative does not exist at x = 0

Alternative Solution:

It is clear from graph f(x) is not differentiable at x = 0.

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