A function is said to be differentiable at a point if the limit which defines the derivate exists at that point.

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Theorem Differentiability Implies Continuity. Example continued Let's calculate the limit for x at the value 0: Such a function is not a continuously differentiable. To be differentiable at a certain point, the function must first of all be defined there!

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So it is not differentiable. The first two are; the third is weaker. In the former case, we sometimes have a cusp on the graph, and in the latter case, we get a point of vertical tangency.

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. PulseJet PulseJet 308 3 8. In common language, you move the secant to form a tangent and it may give you a real tangent at that point, but if you see the tangents around it, they will not seem to be approaching this tangent in any sense.

The definition of continuously differentiable functions Ask Question.

## Differentiable

Return to Main Page Part A: So "continuously differentiable" means "differentiable in a continuous way". ManiAm ManiAm 288 1 2 9. Because when a function is differentiable we can use all the power of calculus when working with it.