Ask Me Help Desk - Finding a vertical tangent when x = ?

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finding a vertical tangent when x = ?

(x^2) - xy + (y^3) = 10 has a vertical tangent when x = ?

I believe I have to take the derivative, by implicit differentiation, but I don't know what to do next. Or I could be wrong..

You're right. Implicit differentiation.

$x^{2}-xy+y^{3}=10$

$2x-(x\cdot\frac{dy}{dx}+y)+3y^{2}\cdot\frac{dy}{dx}=0$

Solve for dy/dx

There's a little trick you can use with implicit diff to make it a little easier.

Find the derivative wrt x. You get $2x-y$ ... [1]

The derivative wrt y. You get $3y^{2}-x$ ... [2]

Now, just use $\frac{-[1]}{[2]}$ . You'll get the same thing.

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