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**what does differentiable at 2 mean**

what does this mean , my question says sketch the graph of a function who has a local maximum at 2 and is differentiable at 2,

what does it mean by it is differentiable at 2,

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- #1

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what does this mean , my question says sketch the graph of a function who has a local maximum at 2 and is differentiable at 2,

what does it mean by it is differentiable at 2,

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does this mean that the slope is 0 at 2

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well if u need to know what this means, it means if it is differentiable at 2 it is continous at 2

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2 formulas below are definition of continous and differentiable properties of a funtion, for example,F(x) :

+ F(x) is continous at x0 <=> limit of F(x) when x->x0 is equal to F(x0)

+ F(x) is differentiable at x0 <=> limit of [F(x)-F(x0)]/[x-x0] when x->x0 exists (that value is so called F'(x0) )

Anyway, note that : "differentiable" and "continous" is not equivalent. "continous" if differentiable, but if "continous", we can't conlude it is differentiable.

If you have anymore question, feel confidently to ask me.

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Gib Z

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Yes. It also means it is continuous at 2. Seeing as they had a parabola, it seems this function is one where the domain is limited.does this mean that the slope is 0 at 2

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