Find the coordinates of the point in the first quadrant at which the tangent line to the curve (x)^3-xy+(y)^3 =0 is parallel to the x axis.

Differentiate implicitly:


Solve for y


When the tangent is parallel to the x-axis we have y'=0, so we must solve


To find the actual value of x we plug this expression for y into the original equation


Plugging this into the formula for y above gives the points


which is where our tangent will be parallel to the x-axis.