I'm asked to find the derivative of f(x)=x|x| at the point (0,0).

Would I do this using the definition of absolute value? o_O

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- November 20th 2008, 02:02 PMbimroccoderivative of |x|
I'm asked to find the derivative of f(x)=x|x| at the point (0,0).

Would I do this using the definition of absolute value? o_O - November 20th 2008, 02:31 PMTwighi
Uhm, is it meant to say , and not

?

is not differentiable in x = 0.

does not exist in x = 0. - November 20th 2008, 02:42 PMbimrocco
- November 20th 2008, 02:46 PMelizsimca
I would start this problem by piecewise defining , which I think is what you meant by the definition of the absolute value. Then take the derivatives of each piecewise defined function. Looking at the graph of will reveal that the function has no "problems" at x=0, i.e. it is continuous and smooth in the neigborhood surrounding the point x=0.

Hope this helps.

(P.S. I'm not sure if this is correct but this is where I would start if I were doing the problem) :) - November 20th 2008, 02:48 PMPlato
Do you see that ?

You should take a good look at the graph of .