Find the equation of the tangent line

[meeklobraca]

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?

 

[slider142]

Looks good, however, at the point (x,y) = (2/3, 4/3), the slope of the graph is 4/5, not -1/2.

 

[Dick]

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.

 

[meeklobraca]

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

 

[slider142]

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

Perfect. :)