Find the equation of the tangent line

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Homework Help Overview

The problem involves finding the equation of the tangent line to the curve defined by the equation 3xy = x^3 + y^3 at the point (2/3, 4/3). The subject area includes calculus, specifically the application of derivatives to determine slopes of tangent lines.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the derivative and subsequently the slope at the specified point, leading to a proposed equation for the tangent line. Some participants question the accuracy of the calculated slope, suggesting a different value. Others express agreement with the questioning of the original poster's calculations.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's calculations and suggesting corrections regarding the slope. There is no explicit consensus on the final equation, as different values for the slope have been proposed.

Contextual Notes

Participants are navigating potential errors in the calculation of the slope and the implications for the tangent line equation. The original poster's approach is being scrutinized, particularly regarding the handling of ratios and fractions.

meeklobraca
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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?
 
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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.
 
slider142 said:
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.
 
Thank you for the help guys, I got 4x - 5y + 4 = 0 for the equation. What do you think?
 
meeklobraca said:
Thank you for the help guys, I got 4x - 5y + 4 = 0 for the equation. What do you think?

Perfect. :)
 

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