given the function the function:

$\displaystyle f(x) = xsinx$

we must find its maxima, minima and inflection pts and show that all these pts belong to four distinct curves of equation:

$\displaystyle \frac{x^2}{\sqrt{1+x^2}}$; $\displaystyle -\frac{x^2}{\sqrt{1+x^2}}$; $\displaystyle \frac{2x}{\sqrt{4+x^2}}$; $\displaystyle -\frac{2x}{\sqrt{4+x^2}}$

the maxima minima values are kinda easy. its the inflection points that are, first of all hard to find, and then prove that they belong to two of the curves (the last two).

can anybody come up with some hints to point me in the right direction.

thanks.