f(x) = 2x^3 + x^2 + 2x We just got into this so haven't gone into great depths so with a problem like this I'm a bit confused. I found f'(x) 6x^2 + 2x + 2 Since all these terms had a 2 common, I divided each term by 2 to get 3x^2 + x + 1 I know the goal is to factor down as much as possible but I don't think this can be factored down any further (when it comes to factoring I'm not the best at it...mainly when it involves coefficients out in front of the term raised to a power). Anyways...the step after you get it factored as much as possible is to set the equation to zero and do the math and you get your critical points. Did I do right by dividing each term by 2 or should I have done something differentl?
f(x) = 2x3 + x2 + 2x Critical Points: f '(x) = 0: f '(x) = 6x2 + 2x + 2 6x2 + 2x + 2 = 0 Dividing each term by 2, 3x2 + x + 1 = 0 3x2 + x = - 1 3(x2 + 1/3 x) = - 1 x2 + 1/3 x = - 1/3 Completing the square, x2 + 1/3 x + 1/36 = 1/36 - 1/3 (x + 1/6)2 = 1/36 - 12/36 (x + 1/6)2 = - 11/36 x + 1/6 =