Implicit Differentiation

[sweetmanda_4]

Find the points at which the graph of the equation 4x^2+y^2-8x+4y=o has a horizontal or vertical tangent

I've gotten the derivative
dy/dx= (4-8x)/2y
But I'm unsure how to do the other parts of the problem! HELP PLEASE!

 

[Deleted member 4993]

Find the points at which the graph of the equation 4x^2+y^2-8x+4y=o has a horizontal or vertical tangent

I've gotten the derivative
dy/dx= (4-8x)/2y............ incorrect
But I'm unsure how to do the other parts of the problem! HELP PLEASE!

\(\displaystyle 8x + 2y\frac{dy}{dx} - 8 + 4\frac{dy}{dx} = 0\)

\(\displaystyle \frac{dy}{dx} \ = \ \frac{8 - 8x}{2y + 4}\)

Where is the derivative = 0?

Where is the derivative = undefined?