Tiana Hill

2022-09-06

I'm stuck on this implicit differentiation question, where I'm requiblack to find the turning points, the equation goes like this ${y}^{3}+3x{y}^{2}-{x}^{3}=3$

Corbin Hanson

Beginner2022-09-07Added 10 answers

I don't know what you mean by turning points, but to find the derivative of your implicit function,

$\mathrm{d}y3{y}^{2}+3{y}^{2}\mathrm{d}x+6yx\mathrm{d}y-3{x}^{2}\mathrm{d}x=0\Rightarrow \frac{\mathrm{d}y}{\mathrm{d}x}=\frac{3{x}^{2}-3{y}^{2}}{3{y}^{2}+6xy}$

Solving for $\frac{\mathrm{d}y}{\mathrm{d}x}$ as you would any other variable.

$\mathrm{d}y3{y}^{2}+3{y}^{2}\mathrm{d}x+6yx\mathrm{d}y-3{x}^{2}\mathrm{d}x=0\Rightarrow \frac{\mathrm{d}y}{\mathrm{d}x}=\frac{3{x}^{2}-3{y}^{2}}{3{y}^{2}+6xy}$

Solving for $\frac{\mathrm{d}y}{\mathrm{d}x}$ as you would any other variable.

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