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Math Help - Derivative of function f(x)=x|x|

  1. #1
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    For the function f(x)=x|x|, show that f'(0) exists. wht is the value?
    Last edited by alexprem; August 9th 2010 at 09:46 PM.
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  2. #2
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    f(x)= |x| = x, x\geq 0 \implies f'(x)=1

    f(x)= |x| = -x, x< 0 \implies f'(x)=-1

    Maybe use the product rule from here?
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  3. #3
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    |x| is not differentiable at x = 0, so what makes you think that x|x| is differentiable there?
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    x|x| = sgn(x) * x^2
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  5. #5
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    f'(0)= \lim_{h\to 0}\frac{f(h)- f(0)}{h}

    For f(x)= x|x|, this is f'(0)= \lim_{h\to 0}\frac{h|h|- 0}{h}= \lim_{h\to 0}|h|= 0.

    Yes, Prove It, even though |x| is not differentiable at x= 0, x|x| is!
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  6. #6
    Senior Member eumyang's Avatar
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    Posted by pickslides from this thread:
    http://www.mathhelpforum.com/math-he...on-153220.html
    Wow this is really similar to http://www.mathhelpforum.com/math-he...on-153221.html

    Are you in the same class or the same person?
    Interesting... Here is another instance of alexprem and ilovemymath posting the exact same question.

    http://www.mathhelpforum.com/math-he...ve-153114.html

    Coincidence?
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  7. #7
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    might be someone from my class
    because we are taking this over online so many of us will have problem as we are not being taught anything
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  8. #8
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    Quote Originally Posted by ilovemymath View Post
    might be someone from my class
    because we are taking this over online so many of us will have problem as we are not being taught anything
    ... such is the major pitfall of "online" classes ... we see many who come here with little or no background in the subject matter for the course they are attempting. I seriously question their academic value.
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