For the function

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For the function

f(x)=|x|

, determine whether the derivative exists at

x = 0

. Give reasons based on the left-hand and right-hand derivatives.

Related theory

Derivative Foundations
Differentiability
Differentiability of functions
Continuity and Differentiability

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