anonymous
  • anonymous
What is the derivative of: 3x^4 - 2x^3 - 12x^2 + 18x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
What'd you come up with? It's a pretty straight forward derivative to take.
anonymous
  • anonymous
what i am wondering is if i should take an x out first. x(3x^3 - 2x^2 - 12x +18)
anonymous
  • anonymous
Oh, no. Take the derivative term by term. It'll be much simplier.

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anonymous
  • anonymous
thanks
anonymous
  • anonymous
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
  • anonymous
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
  • anonymous
\[f' = 12x^3 -6x^2 - 24x + 18\] \[f' = 0 \implies 2x^3 - x^2 - 4x + 3 = 0\]
anonymous
  • anonymous
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
  • anonymous
should have been relative max and rel min
anonymous
  • anonymous
with having so many x's i am not sure how to find the critical points
anonymous
  • anonymous
Yeah it's a tough one to factor.
anonymous
  • anonymous
should i pull an x out before i get the derivative
anonymous
  • anonymous
We can try..
anonymous
  • anonymous
I'm not sure it'll make it better.
anonymous
  • anonymous
i had done that already and it still has alot of x's
anonymous
  • anonymous
It pretty much gives the same result. I was hoping it would be of a form that would better suggest how to factor.
anonymous
  • anonymous
\(2x^3−x^2−4x+3=0\) \(x^2(2x-1) -(2x - 1) - (2x -1) -1\)
anonymous
  • anonymous
Bleh. I need to practice dividing polynomials more apparently ;p
anonymous
  • anonymous
WA claims it's \((x-1)^2(2x+3)\)
anonymous
  • anonymous
thanks for your help. i will work on this again tomorrow
anonymous
  • anonymous
one more quick question. should i go ahead and get the second derivative before i can get the critical points.
anonymous
  • anonymous
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.

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