# Implicit Differentiation and coordinates

1. Oct 26, 2008

### Kar91102

1. The problem statement, all variables and given/known data
Find the coordinates of the point in the first quadrant at which the tangent line to the curve x3-xy+y3=0 is parallel to the x-axis.

SO:
x= +
y= +
mtan=0

2. Relevant equations

$$\frac{dy}{dx}=m_{tan}$$

3. The attempt at a solution

$$\frac{dy}{dx}=\frac{y-3x^{2}}{3y^{2}-x}=0$$

After I get the derivative, I have no clue what to do.

2. Oct 26, 2008

### viciousp

you have two equations two variables so solve for one of the variables

3. Oct 26, 2008

### Dick

For the derivative to equal zero x and y must satisfy y-3x^2=0, right? But x and y must also be on the curve so x^3-xy+y^3=0. That's two equations in two unknowns. Solve them.

4. Oct 26, 2008

### HallsofIvy

Staff Emeritus
You now have two equations to solve for x and y. Oh, and here's a simplification:
a fraction is 0 only when its numerator is 0.

Blast! I walked away from the computer and Dick got in ahead of me!