maximum and minimum value question

afcwestwarrior

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,

afcwestwarrior

does this mean that the slope is 0 at 2

afcwestwarrior

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

afcwestwarrior

one more thing how do i sketch this graph, all it gives me is it is continous at 2, does it matter how i sketch this graph, does it have to be a certain type, does it have to look a certain way, in the back of my book it is a parabola and its continous on the negative side

baolkvn

Well, differentiable and continous is not equivalent. continous if differentiable, but if continous, we can't conlude it is differentiable.
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.

Mystic998

Well, strictly speaking, it doesn't have to look particularly normal to satisfy the requirements. But likely for your purposes, you're going to want something that's continuous in an interval around 2 and appears "smooth" at 2 (i.e., it has no sharp edge).

Gib Z

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.