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Derivatives : Find the values of x for any points where the curve 2x^2+xy+3y^2=54 has a vertical tangent.

Find the values of x for any points where the curve 2x^2+xy+3y^2=54 has a vertical tangent.

Choices are:A. (18*(square root of 46))/23, B. (18*(square root of 20))/5, C. (5*(square root of 3))/23, D. (16*(SQAURE ROOT OF 23))/25 OR NONE OF THESE.

Please show work.

Solution Preview

First, we need to compute the derivative y'. Take derivative on both sides, we have

4x+xy'+y+6yy'=0

so,

(x+6y)y'=-4x-y

So,
y'=-(4x+y)/(x+6y) ...

Solution Summary

The values of x for any points where the curve 2x^2+xy+3y^2=54 has a vertical tangent are found.

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