Not possible to find a function g such that g

[squenshl]

Why is it not possible to find a function g such that g \in C¹ at (0,0) and g is not differentiable at (0,0)

 

[squenshl]

Also given that f(x,y) = x|y| how do I show that f \notin C¹ at (0,0)

 

[slider142]

Why is it not possible to find a function g such that g \in C¹ at (0,0) and g is not differentiable at (0,0)

As far as I know, a function is defined to be C¹ if it is continuously differentiable, so the question doesn't make sense.

 

[slider142]

Also given that f(x,y) = x|y| how do I show that f \notin C¹ at (0,0)

Remember the definition of differentiability: all approaches to the point (0,0) must yield the same derivative. Consider approaching the derivative along the x-axis and then the derivative along the y-axis. Are they equal?