Where am I going wrong on implicit differentation?

  • Thread starter jrjack
  • Start date
  • #1
111
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Homework Statement



Determine the equation of a tangent line to a curve at the given point.

3x2+xy+2y2=36 , P(2,3)

Homework Equations





The Attempt at a Solution



3x2+xy+2y2 = 36

finding the derivatives of each term I get:

6x+xy'+y+4yy' = 0
xy'+4yy' = -6x-y
y'(x+4y) = -6x-y
[tex]y' = \frac{-6x-y}{x+4y}[/tex]
Which gives me a slope of 1.5 after plugging (2,3) in to the equation.

Then for the tangent: y-3=1.5(x-2) , y=1.5x

Somewhere I went wrong because this is not the right answer.
 

Answers and Replies

  • #2
662
1
Haven't looked at it carefully, but slope should be -1.5, after substitution.
 
  • #3
1,198
5
Try replugging your point (2,3).
 
  • #4
111
0
[tex]\frac{-6(2)-3}{2+4(3)}=\frac{-15}{14}[/tex]

I copied the wrong sign down.
 
Last edited:
  • #5
1,039
1
if you plug in (2,3) you get -15 / 14 for the slope.
 
  • #6
111
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Thanks for your help, I don't know why I can't seem to find my mistakes when going back through the problem. I even copied it down wrong on here as I was saying right outloud to myself.

Once again Thanks.
 

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