Decoding the 2024 AP Calculus AB Exam: FRQ #5

Consider the curve defined by the equation x^2 + 3y + 2y^2 = 48. It can be shown that dy/dx = -2x/3+4y .
(a) There is a point on the curve near (2, 4) with x-coordinate 3. Use the line tangent to the curve at (2, 4) to approximate the y-coordinate of this point.
(b) Is the horizontal line y = 1 tangent to the curve? Give a reason for your answer.
(c) The curve intersects the positive x-axis at the point (48 , 0). Is the line tangent to the curve at this point vertical? Give a reason for your answer.
(d) For time t ≥ 0, a particle is moving along another curve defined by the equation y^3 + 2xy = 24. At the instant the particle is at the point (4, 2), the y-coordinate of the particle’s position is decreasing at a rate of 2 units per second. At that instant, what is the rate of change of the x-coordinate of the particle’s position with respect to time?
Intro: 0:00
Part A: 0:37
Part B (Method 1): 2:33
Part B (Method 2): 5:22
Part C: 6:32
Part D: 7:55
Score Predictions: 10:18