IMPLICIT DIFFERENTIATION
Differentiate both sides.
[tex]3x^{2} + 4xy + 2x^{2}\frac{dy}{dx} - 4\frac{dy}{dx} = 0[/tex]
[tex]2x^{2}\frac{dy}{dx} - 4\frac{dy}{dx} = -3x^{2} - 4xy[/tex]
[tex]\frac{dy}{dx}(2x^2 - 4) = -3x^{2} - 4xy[/tex]
[tex]\frac{dy}{dx} = \frac{-3x^{2} - 4xy}{2x^2 - 4}[/tex]
When x = 1...
[tex]1^{3} + 2y - 4y = 7[/tex]
[tex]-2y = 6, y = -3[/tex]
[tex]\frac{dy}{dx} = \frac{-3(1)^{2} - 4(1)(-3)}{2(1)^2 - 4}[/tex]
[tex]\frac{dy}{dx} = \frac{-3 + 12}{-2}[/tex]
[tex]\frac{dy}{dx} = -\frac{9}{2}[/tex]
Hence, A should be correct.
