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.