proving differentiability at (0,0)

Asked May 11 '20 at 05:31

Active May 11 '20 at 05:44

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Let F(x,y) be a a two variables function that is continuous in R^2 and differentiable at R^2/({0/0}.

Its partial derviatives(Fx(x,y),Fy(x,y)) at (0,0) both approach zero. I have to prove that the function is differentiable at (0,0).

Which direction should I go ? Should I try proving it using differentiability definition or somehow prove partial derivatives are continuous ?

edited May 11 '20 at 05:44

asked May 11 '20 at 05:31

JustCurious

"continuous on the entire real line" you mean continuous on $\mathbb R^2$ right? – Sarvesh Ravichandran Iyer May 11 '20 at 05:35
Yes, Sorry about the misunderstanding. fixed it. – JustCurious May 11 '20 at 05:37
I will edit your question with MathJax. See how I do it, next time you can do it. – Sarvesh Ravichandran Iyer May 11 '20 at 05:37
Here’s the MathJax tutorial – gen-ℤ ready to perish May 11 '20 at 06:13

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