What is the derivative of:

3x^4 - 2x^3 - 12x^2 + 18x

Question

What is the derivative of:

3x^4 - 2x^3 - 12x^2 + 18x

anonymous · Answer

What'd you come up with? It's a pretty straight forward derivative to take.

anonymous · Answer

what i am wondering is if i should take an x out first.

x(3x^3 - 2x^2 - 12x +18)

anonymous · Answer

Oh, no. Take the derivative term by term. It'll be much simplier.

anonymous · Answer

thanks

anonymous · Answer

In general I find it's easier to multiply out the products and take the derivative term by term unless it's a particularly hairy product with a lot of exponents, etc.

anonymous · Answer

ok, the whole problem is:
Find all critical point of: (the orginal equation i entered) and use the second derivative test to classify each as a relative man and rel min or neither.
it seems to be more difficult to get my critical points.

anonymous · Answer

$$f' = 12x^3 -6x^2 - 24x + 18$$
$$f' = 0 \implies 2x^3 - x^2 - 4x + 3 = 0$$

anonymous · Answer

when you say taking the derivative, I am assuming you mean the derivative with respect to x? Therefore, the derivative would symply be: f'(x)=12x^3-6x^2-24x+18

anonymous · Answer

should have been relative max and rel min

anonymous · Answer

with having so many x's i am not sure how to find the critical points

anonymous · Answer

Yeah it's a tough one to factor.

anonymous · Answer

should i pull an x out before i get the derivative

anonymous · Answer

We can try..

anonymous · Answer

I'm not sure it'll make it better.

anonymous · Answer

i had done that already and it still has alot of x's

anonymous · Answer

It pretty much gives the same result. I was hoping it would be of a form that would better suggest how to factor.

anonymous · Answer

$2x^3−x^2−4x+3=0$
$x^2(2x-1) -(2x - 1) - (2x -1) -1$

anonymous · Answer

Bleh. I need to practice dividing polynomials more apparently ;p

anonymous · Answer

WA claims it's $(x-1)^2(2x+3)$

anonymous · Answer

thanks for your help. i will work on this again tomorrow

anonymous · Answer

one more quick question.
should i go ahead and get the second derivative before i can get the critical points.

anonymous · Answer

i really dont think i will. i think i get the critical points from the first derivative and then i get the second derivative to test.