Consider the curve given by X^2+4y^2=7+3xy
a) show that dy/dx=3y-2x/8y-3x
b) show that there is a point P with x-cooridnate 3 at which the line tangent to the curve at P is horizontal. Find the y-cooridnate of P.
c)find the value of d^2y/dx^2 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 your answer.
(a) is easy. All you do is find the derivative.
For (b), I got the point (3,2) by plugging 3 into the original equation and got 2.
For (c), the value I got was -2/7 by finding the second derivative and plugging (3,2) for the x's and y's. I need to know if this is right and if there are any max's or min's at this point. Thanks.