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11TH•Mathematics•Differentiation•13.3 Differentiation Theorems

13.5 Differentiability and Continuity

Differentiability implies continuity; constant, sum, product, and quotient rules.

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13.5 Differentiability and Continuity

If ff is differentiable at a point, then ff is continuous there. The converse fails: f(x)=∣x∣f(x) = |x| is continuous at 00 but not differentiable (left derivative −1-1, right derivative 11).

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13.2 Differentiation from First Principles
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13.4 Applications of Differentiation