Free-Response
Part A
AB1. (a) Since x^2 y − 3y^2 = 48,
(b) At (5,3), so the equation of the tangent line is(c)
(d) Horizontal tangent lines have This could happen only if
2 xy = 0, which means that x = 0 or y = 0.
If x = 0, 0y − 3y^2 = 48, which has no real solutions.
If y = 0, x^2 · 0 − 3 · 0^2 = 48, which is impossible. Therefore, there are no horizontal
tangents.