Differentiability

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Cegep1

Mathematics

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110 words

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1 minute

Quality of a function:

• At a point $a$ if $\underset{h\to 0}{lim}\frac{f(a+h)-f(a)}{h}$ (derivative at $a$) exists
• Over an open interval if every point of the interval is differentiable
• Over a closed interval if the open interval is differentiable and the left / right endpoints are right / left differentiable

Implies continuity

Sidedness

Left differentiability at $a$ if $\underset{h\to 0^{-}}{lim}\frac{f(a+h)-f(a)}{h}$ (left-side derivative at $a$) exists
Right differentiability at $a$ if $\underset{h\to 0^{+}}{lim}\frac{f(a+h)-f(a)}{h}$ (right-side derivative at $a$) exists

Contributors

Ajitani Hifumi

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