For the function f(x)=x|x|, show that f'(0) exists. wht is the value?

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- Aug 9th 2010, 09:12 PMalexpremSolved
For the function f(x)=x|x|, show that f'(0) exists. wht is the value?

- Aug 9th 2010, 09:25 PMpickslides
$\displaystyle f(x)= |x| = x, x\geq 0 \implies f'(x)=1 $

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

Maybe use the product rule from here? - Aug 9th 2010, 09:58 PMProve It
$\displaystyle |x|$ is not differentiable at $\displaystyle x = 0$, so what makes you think that $\displaystyle x|x|$ is differentiable there?

- Aug 9th 2010, 09:58 PMAlso sprach Zarathustra
x|x| = sgn(x) * x^2

- Aug 10th 2010, 03:06 AMHallsofIvy
$\displaystyle f'(0)= \lim_{h\to 0}\frac{f(h)- f(0)}{h}$

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

Yes, Prove It, even though |x| is not differentiable at x= 0, x|x| is! - Aug 10th 2010, 04:23 AMeumyang
Posted by pickslides from this thread:

http://www.mathhelpforum.com/math-he...on-153220.html

Quote:

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?

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

Coincidence? (Wondering) - Aug 10th 2010, 10:34 AMilovemymath
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 - Aug 10th 2010, 11:28 AMskeeter