Given the equation:

$\displaystyle f(x)=1+x-\frac{x^2}{1}-\frac{x^3}{1}$

I want to find the x-value of the top point of this equation, which as a graph I've found to be $\displaystyle x=\frac{1}{3}$

However when I try to find this value, I don't end up with $\displaystyle \frac{1}{3}$

First I differentiate the equation:

$\displaystyle f'(x)=\frac{d}{dx}1+x-\frac{x^2}{1}-\frac{x^3}{1}=1-2\cdot x-3\cdot x^2$

Now I put the differentiated equation equal to 0 and isolate x:

$\displaystyle 1-2\cdot x-3\cdot x^2=0$

$\displaystyle x=-1$