For , define . Determine all real values of for which is continuous at but not…

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

Problem

For

k>0

, define

h_k(x)=|x|^{\,k}

. Determine all real values of

k

for which

h_k

is continuous at

x=0

but not differentiable there.

Related theory

Derivative Foundations
Differentiability
Differentiability of functions
Continuity and Differentiability

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