Could someone please help with this:
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.

Question

Could someone please help with this:
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.

anonymous · Answer

you need to find the derivative implicitly.  It is very difficult to solve for y, so treat it as a differentiable function.  The derivative of the first and last terms are 3x to the second and 3y to the second times dy/dx.  This is the chain rule.  The middle term is a product rule so it is 1y plus x times dy/dx.  Now you can solve for dy/dx, then find values for which it is equal to zero.  Then find the corresponding value of the other variable in the original function.