Consider curve given by

Question

x^2+ 4y^2= 7 + 3xy..

Three part question
A) show that dy/dx = 3y-2x/8y-3x

B) Show that there is a point P with
x-coordinate 3 at whiich the line tangent to the curve at P is horizontal. Find the y-coordinate of P.

C) find the value of d^2y/ dx^2 at the point p found in part (B)

Answer 1

2x dx+8ydy=3ydx + 3xdy

solve for dy/dx

Then, take the next derivative.
for B), put x=3 into the original equation, find y. Then find the slope (dy/dx) at that point.