Implicit Differentiation and coordinates

[Kar91102]

Homework Statement

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= +
m_tan=0

Homework Equations

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

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.

 

[viciousp]

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

 

[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.

 

[HallsofIvy]

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!