How to invent a function F: R2 to R such that fx(1,1) and fy(1,1) both exist, but f is not differentiable at (1,1). Prove the function satisfies the conditions.
I have tried and always come up the function that is differentiable at (1,1) with existing fx(1,1) and fy(1,1), ilike f(x,y)=(x-1)(y-1). If it's not differentiable, fx(1,1) and fy(1,1) not exist. How do I find a function that exist at fx(1,1) and fy(1,1) but is not differentiable/.
Thanks.
I have tried and always come up the function that is differentiable at (1,1) with existing fx(1,1) and fy(1,1), ilike f(x,y)=(x-1)(y-1). If it's not differentiable, fx(1,1) and fy(1,1) not exist. How do I find a function that exist at fx(1,1) and fy(1,1) but is not differentiable/.
Thanks.