Not possible to find a function g such that g

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If not, the function is not differentiable at (0,0). In summary, a function cannot be C1 and not differentiable at the same point, and we can show that f(x,y) = x|y| is not C1 at (0,0) by examining its derivatives along different axes.
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squenshl
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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)
 
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Also given that f(x,y) = x|y| how do I show that f [tex]\notin[/tex] C1 at (0,0)
 
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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.
 
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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?
 

1. Is it really not possible to find a function g?

Yes, it is not possible to find a function g in certain cases. There are many mathematical problems that have been proven to have no solution or no function that can accurately solve them. This can be due to the complexity of the problem or limitations in our current understanding and technology.

2. Why is it not possible to find a function g?

There are many reasons why it may not be possible to find a function g. It could be because the problem is unsolvable, the data is insufficient, or the variables involved are too complex. It could also be due to limitations in our knowledge and understanding of mathematics.

3. Can't we just keep searching for a function g until we find one?

In theory, we could keep searching for a function g, but there is no guarantee that we will find one. Some problems are proven to be unsolvable, and no amount of searching will change that. It is also important to consider the time and resources required for such a search, which may not be feasible.

4. Are there any alternatives to finding a function g?

Yes, there are alternative approaches to solving problems that do not involve finding a function g. These may include using approximation methods, numerical methods, or even changing the problem to make it solvable. It is important to consider all options when faced with a problem that seems impossible to solve.

5. Will it ever be possible to find a function g?

It is impossible to say for certain if it will ever be possible to find a function g for a particular problem. As our knowledge and technology continue to advance, it is possible that we may find a solution or a function that can accurately solve the problem. However, there may also be problems that are fundamentally unsolvable, and in those cases, it will never be possible to find a function g.

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