Does g(x) = x|x| have an inflection point at (0;0) and g''(0) does not exist?

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Homework Statement


show that g(x)= x|x| has an inflection point at (0;0) and g'' (0) Does not exist


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The Attempt at a Solution

 
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I can see what they mean. Can you?

Having seen what they mean I can afford to treat this problem with the contempt it deserves.
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But you can't.

So what you will have to do is look up the definitions.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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