Question

Determine the critical points of the following function on \[R\]
\[f(x)=x^{4}+2x^{3}-2x^{2}+1\]

Answer 1

\[f'(x)=2x+6x^2-4x=6x^2-2x=0---->\]

Answer 2

can u solve for x now

Answer 3

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

Answer 4

now its ok...

Answer 5

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

Answer 6

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

Answer 7

\[4x^3+6x^2-4x=0..x(4x^2+6x-4)=0......solve\]

Answer 8

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...