Question

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

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

Answer 1

No critical numbers

Explanation:

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]}