Prove that $f(x)=|x|$ is not differentiable at $x=0$.

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Lesson Parent: 
Differentiation II: The Gory Details of Calculating Derivatives
Problem: 

Prove that $f(x)=|x|$ is not differentiable at $x=0$.

Answer: 

$f(x)=|x|$ is not differentiable at $x=0$.

SAMPLE SOLUTION

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Solution: 

The derivative of <Sign in to see all the formulas> at $x=0$ is given by

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But we have shown here that this limit does not exist. Therefore, $f'(x)$ does not exist at $x=0$.