anonymous
  • anonymous
Math help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
should be where dy/dx is undefined. Do you have a derivative?
anonymous
  • anonymous
3x^2-2y+2x
anonymous
  • anonymous
When you take the derivative of y² you have to use the chain rule/implicit differentiation, so multiply by dy/dx. Now solve for dy/dx 3x² - 2y(dy/dx) + 2x = 0

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anonymous
  • anonymous
So would it just be 2?
anonymous
  • anonymous
no. where did you get 2?
anonymous
  • anonymous
or how I should say?
anonymous
  • anonymous
I thought you would just derive 2y to get 2
anonymous
  • anonymous
oh ok. You actually have to solve the equation derivative for dy/dx by moving everything else to the other side. \[3x^2-2y \frac{ dy }{ dx }+2x=0\]
anonymous
  • anonymous
So I would get -2y by itself by moving 3x^2 and 2x to the other side?
anonymous
  • anonymous
yes
anonymous
  • anonymous
So I would get -2ydy/dx=-3x^2-2x?
anonymous
  • anonymous
right. Now divide by -2y
anonymous
  • anonymous
So it would be 3x^2/2y+x/y
anonymous
  • anonymous
yes :) BUT it's easier to keep it as one fraction because you need to find the undefined locations and it's just easier with one fraction instead of multiples, especially on more complex problems. \[\frac{ dy }{ dx }=\frac{ 3x^2+2x }{ 2y }\] since we're looking for vertical tangent lines we need where dy/dx is undefined. That would be where the denominator is 0
anonymous
  • anonymous
Would I have to do the quotient rule for this?
anonymous
  • anonymous
no. just 2y = 0 to get the y-value
anonymous
  • anonymous
Y would equal 0 then
anonymous
  • anonymous
yes. then plug that into the original equation to find the x-coordinates
anonymous
  • anonymous
So the point would be (0,0)?
anonymous
  • anonymous
that's one of them. There's another x³ + x² = 0 x²(x + 1) = 0
anonymous
  • anonymous
(-1,0)?
anonymous
  • anonymous
yep :)
anonymous
  • anonymous
Okay thank you!
anonymous
  • anonymous
you're welcome!

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