(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a) If 2y^{2}-xy-x^{2}=0 , find dy/dx.

b) What is/are the slope(s) of the tangent(s)at x=1?

2. Relevant equations

3. The attempt at a solution

Using implicit differentiation:

a) (4y)dy/dx-(x)dy/dx-y(1)-2x=0

(4y)dy/dx-(x)dy/dx=2x+y

(4y-x)dy/dx=2x+y

dy/dx=(2x+y)/(4y-x)

Assuming that I found dy/dx correctly (please let me know if I did not) I am having some trouble seeing where to go from here to complete part b). If I had x and y coordinates I could work through it but with only an x value it is proving difficult for me.

My latest attempt was to try and solve for y using the original equation.

b) 2y^{2}-xy-x^{2}=0

At x=1, 2y^{2}-(1)y-(1)^{2}=0

Leaving me with:

2y^{2}-y=1

And that's where I ended up, stuck and admittedly confused.

Any help or nudges in the right direction would be greatly appreciated.

Thanks,

-Trevor

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# Find dy/dx and then find slope of tangent(s).

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