Show that is continuous but not differentiable at

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

Problem

Show that

f(x)

is continuous but not differentiable at

x = 0

, where:

Condition	$f(x)$
$x \neq 0$	$x \sin \frac{1}{x}$
$x = 0$	$0$

Related theory

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

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