Find the equation of the tangent line

  • #1
189
0

Homework Statement



Find the equation of the tangent line to the curve 3xy = x^3 + y^3 at point (2/3,4/3)


Homework Equations





The Attempt at a Solution



I found the deriviative to be 3x^2-3y / 3x - 3y^2 which i simplified to x^2 - y / x - y^2

I found the slope of at those points to be - 1/2

Then using the y - y1 = m(x - x1) formula I got 3x + 3y - 10 = 0 for the equation.

What do you guys think?
 

Answers and Replies

  • #2
1,015
70
Looks good, however, at the point (x,y) = (2/3, 4/3), the slope of the graph is 4/5, not -1/2.
 
  • #3
Dick
Science Advisor
Homework Helper
26,263
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Looks good, however, at the point (x,y) = (2/3, 4/3), the slope of the graph is 4/5, not -1/2.

I agree. I think you are having problems with ratios of fractions.
 
  • #4
189
0
Thank you for the help guys, I got 4x - 5y + 4 = 0 for the equation. What do you think?
 
  • #5
1,015
70
Thank you for the help guys, I got 4x - 5y + 4 = 0 for the equation. What do you think?

Perfect. :)
 

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