Implicit Derivative at a Point

Question

If 1 + 3y = xy then find the equations of all tangent lines to the curve when x=2

Answer 1

Estefani, my advice is to treat implicit just like regular:

given 1 + 3y= xy take the derivative of both sides--product rule for the right side

0 + 3(dy/dx) = (1)(dx/dx)(y) + (x) (1) (dy/dx)

3 dy/dx= y + (x) (dy/dx)

then solve for dy/dx

3(dy/dx) - (x) (dy/dx) = y

dy/dx = (y)/(3 - x)

now you should be able to find tangent lines using point-slope form

Hope this helps--Andrew

Answer 2

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