I am working a problem on mathlab. It looks straightforward until I apply the quadratic formula and I get a negative number under a square root, which isn't allowed.

Locate the critical points of the function $\displaystyle f(x)=x^3+4x^2+9x+1$

the derivative is $\displaystyle f'=3x^2+8x+9$

Critical points are when F'=0, so I apply the quadratic formula to find the CP's.

$\displaystyle \frac{-(8) + or - \sqrt{8^2 - 4(3)(9)}}{2(3)}$

this will simply to

$\displaystyle \frac{-8+ \sqrt{-44}}{6}$ and $\displaystyle \frac{-8-\sqrt{-44}}{6}$

The negative number in the sqrt doesn't make sense.