find the critical numbers of $f(x) = 2x^3+x^2+2x$ ?

Question

I have differentiated the equation to $6x^2+2x+2$ but need help in the next steps

8198 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-23T12:31:00

No critical numbers

Critical values occur when $dy/dx=0$

$6x^2+2x+2=0$

$3x^2+x+1=0$

$x=(-1+-sqrt(1^2-4(3)))/6$

$x=(-1+-sqrt(1-12))/6$

$x=(-1+-sqrt(-11))/6$

$x=(-1+isqrt(11))/6or(-1-isqrt(11))/6$

$f'(x)>0$

No critical numbers.

Graph:

graph{2x^3+x^2+2x [-7.9, 7.9, -3.95, 3.95]}