SOLUTION: Determine the slope of the curve at the given point.find the equation of the tangent line at the given point. y(3x-y^2)=16 at (4,2)

Question 1136444: Determine the slope of the curve at the given point.find the equation of the tangent line at the given point.
y(3x-y^2)=16 at (4,2)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Determine the slope of the curve at the given point.find the equation of the tangent line at the given point.
y(3x-y^2)=16 at (4,2)
========================
y(3x-y^2)=16
y^3 - 3xy = -16
Differentiate implicitly.
----
3y^2*dy - 3x*dy - 3y*dx = 0
(3y^2* - 3x)*dy = 3y*dx
(y^2* - x)*dy = y*dx
dy/dx = y/(y^2 - x)
=======================
dy/dx = 2/(4 - 4)
---> infinite slope
-----------------------
find the equation of the tangent line at the given point.
x = 4

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