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differentiate Find the points on the graph $\displaystyle x^3 + y^3 = xy $
that are parallel to the x axis (gradient = 0)
so I have to differentiate it
I had
$\displaystyle 3x^2 + 3y^2 (dy/dx) = dy/dx $
correction, product rule on the right hand side ...
$\displaystyle \textcolor{red}{3x^2 + 3y^2 \frac{dy}{dx} = x \frac{dy}{dx} + y}$
then what? solve for $\displaystyle \textcolor{red}{\frac{dy}{dx}}$ and set the derivative equal to 0. use that equation to find a relationship between y and x to find the points on the curve where the gradient is 0.