1. ## Critical points

Ok I've worked on these for a while and can't seem to come up with the right answer. Can someone help me out?

1. f(x) = x^2/1-x
Find the critical points

2. f(x) = x^6 - 3x^4 + 3x^2 - 1
Find the critical points

Were also asked to find the domain, intercepts, symmetry and asymptotes. I'm pretty sure there aren't asymptotes for either one, and I'm pretty sure I got the answers to the others. If you want to answer those to to verify my answers that would be great. Thanks!

2. I can see your first mistake , "there are no asymptotes", there is an asymptote for $f(x)=\frac{x^2}{1-x}$ at $x=1$ with $\lim_{x\to 1^-} f(x) = +\infty$ and $\lim_{x\to 1^+}f(x) = -\infty$. However, there are no horizontal asymptotes because $\lim_{x\to \infty}f(x) =\lim_{x\to -\infty}f(x) = +\infty$.

3. To find the critical points, take the derivative of the function and set it equal to 0. Then solve for x.

1. f(x) = x^2/1-x
$
f'(x) = \frac {2x(1-x)-(-1)x^2}{(1-x)^2} = 0$

$
\frac {2x-2x^2+x^2}{(x-1)^2} = 0$

$2x-x^2 = 0, x \not = 1$
x=2,0

So the critical points are (2,f(2)) and (0, f(0))
So the final answer is (2,-4) and (0, 0)

I will leave you to do the second question