Question

Use implicit differentiation to find the slope of the tangent line to the curve 4 x^2 - 3 xy + 4 y^3 = -113 at the point ( -1,-3 ).

Answer 1

f'(x, y) = 8x -3xydy/dx +12y²dy/dx = 0
(12y² -3xy)dy/dx = -8x
dy/dx = -8x/[12y² -3xy]
dy/dx |(x=-1 , y=-3) : = -8(-1)/[12(-3)² - 3(-1)(-3)]
= 8/[108 -9]
=8/99