anonymous 4 years ago Determine the critical points of the following function on $R$ $f(x)=x^{4}+2x^{3}-2x^{2}+1$

1. anonymous

$f'(x)=2x+6x^2-4x=6x^2-2x=0---->$

2. anonymous

can u solve for x now

3. anonymous

i am sorrry i wrote wrong..i edit the question just a minute pls

4. anonymous

now its ok...

5. anonymous

do it the sameway differentiate and equate to 0 and solve for x

6. anonymous

$f'(x) = 4x^{3}+6x^{2}-4x$ $f''(x) = 12x^{2}+12x-4$ and now ?

7. anonymous

$4x^3+6x^2-4x=0..x(4x^2+6x-4)=0......solve$

8. anonymous

there is in solution following numbers $x_{1}=-\frac{-3-\sqrt{15}}{4}$ $x_{2}=0$ $x_{3}=\frac{-3+\sqrt{15}}{4}$ but i dont understand how its possible to find this solutions...