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MIT 18.01 Single Variable Calculus (OCW) 44 Online
OpenStudy (anonymous):

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.

OpenStudy (anonymous):

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.

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