## Calculus 8th Edition

Find the critical numbers for $f(x) = 2x^3+x^2+2x$ Differentiate and set the derivative $=0$ $f'(x) = 6x^2+2x+2$ $0=2(3x^2+x+1)$ $b^2-4ac = 1-4(3)(1) = -11$ The discriminant of the right hand side quadratic is $<0$. Therefore, the right hand side will never $=0$, so $f(x)$ has no critical numbers.