# Thread: Non-real critical values possible?

1. ## Non-real critical values possible?

The question in question:

Find the critical numbers of the function $\displaystyle f(x)=2x^3+x^2+2x$.

I know that $\displaystyle f'(x)=6x^2+2x+2=2(3x^2+x+1)$.

Solving using the quadratic formula gives me $\displaystyle x=\frac{-1\pm\sqrt{11}i}{6}$

I'm only taking Calc 1, so I figured that I should just say that there aren't any critical values, but do non-real values count?

2. ## Re: Non-real critical values possible?

Originally Posted by beebe
The question in question:

Find the critical numbers of the function $\displaystyle f(x)=2x^3+x^2+2x$.

I know that $\displaystyle f'(x)=6x^2+2x+2=2(3x^2+x+1)$.

Solving using the quadratic formula gives me $\displaystyle x=\frac{-1\pm\sqrt{11}i}{6}$

I'm only taking Calc 1, so I figured that I should just say that there aren't any critical values, but do non-real values count?
not if you're studying calculus of a real variable (which you most probably are)