Help me with math please
The graph of the equation y^4=y^2-x^2 is given.
a) verify that dy/dx = (2x)/(2y-(4y^3)). Show why.
b) Find the point(s) (x,y) at which the graph has a horizontal tangent line. Show why/work.
c) Find the y-value(s) at which the graph has a vertical tangent line. Show why/work.
d) While the graph exists at (0,0), the slope does not. Using dy/dx, explain why this is so.
2.Consider the curve given by 6+x^3y=xy^2
a) show that dy/dx =(y^2-3x^2y)/(x^3-2xy)
b) find every point(s) on the graph of the curve that has an x-coordinate of 1, then write an equation for the tangent line at every/each of these point(s).
c) The graph of the curve has vertical tangent lines. Find the x-coordinate of each of these vertical tangent lines. Show why/work.