Big homework assignment this week, and luckily i was able to do most of the problems. However, there are these 3 that i just can't go right.

1. Equation is $\displaystyle 2(y^3) + 6(x^2)y- 12(x^2) + 6y = 1$

a. Show that the derivative of the above equation is equal to $\displaystyle (4x -2xy)/(x^2 + y^2 + 1)$

b. Write an equation of each horizontal tangent line to the curve.

c. The line through the origin with slope -1 is tangent to the curve at point P. Find the x and y coordinates of point P.

2. Equation is $\displaystyle x^2 + 4(y^2) = 7 = 3xy$

a. Show that the derivative of the above equation is equal to $\displaystyle (3y - 2x)/(8y - 3x)$

b. Show that there is a point P with x coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y coordinate of P.

c. Find the value of the second derivative at the point P found in part b. Does the curve have a local maximum, a local minimum, or neither at the point P? Justify.

3. Equation is $\displaystyle x(y^2) - (x^3)y = 6$

a. Show that the derivative of the above euation is equal to $\displaystyle (3(x^2)y - Y^2)/(2xy - x^3)$

b. Find all the points on the curve whose x coordinate is 1, and write an equation for the tangent line at each of these points.

c. Find the x coordinate of each point on the curve where the tangent line is vertical.

Not easy, i know! Hopefully someone can help me out with some of these. Thanks in advance!!!!