Consider the function

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

Problem

g(x)=|x-2|^{3}

. (i) Verify that

g

is continuous at

x=2

. (ii) Find

g'(2)

and hence state whether

g

is differentiable at

x=2

Related theory

Continuity at a Point
Continuity
Derivative Foundations
Differentiability
Differentiability of functions
Continuity and Differentiability

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