Not possible to find a function g such that g

squenshl · Jul 31, 2009

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

squenshl · Jul 31, 2009

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

slider142 · Jul 31, 2009

squenshl said:

Why is it not possible to find a function g such that g [tex]\in[/tex] 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 · Jul 31, 2009

squenshl said:

Also given that f(x,y) = x|y| how do I show that f [tex]\notin[/tex] 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?

Not possible to find a function g such that g

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