- #1

- 457

- 0

**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,

Last edited:

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter afcwestwarrior
- Start date

- #1

- 457

- 0

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,

Last edited:

- #2

- 457

- 0

does this mean that the slope is 0 at 2

- #3

- 457

- 0

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

- #4

- 457

- 0

- #5

- 4

- 0

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.

- #6

- 206

- 0

- #7

Gib Z

Homework Helper

- 3,346

- 6

does this mean that the slope is 0 at 2

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.

Share: