Скачать или смотреть 2024 AP Calculus AB FRQ #3

The depth of seawater at a location can be modeled by the function H that satisfies the differential equation dH/dt = 1/2 (H - 1) * cos(t/2), where H(t) is measured in feet and t is measured in hours after noon (t = 0). It is known that H(0) = 4.

(a) A portion of the slope field for the differential equation is provided. Sketch the solution curve, y = H(t), through the point (0, 4).

(b) For t is between 0 and 5, it can be shown that H(t) is greater than 1. Find the value of t, for t is between 0 and 5, at which H has a critical point. Determine whether the critical point corresponds to a relative minimum, a relative maximum, or neither a relative minimum nor a relative maximum of the depth of seawater at the location. Justify your answer.

(c) Use separation of variables to find y = H(t), the particular solution to the differential equation dH/dt = 1/2 (H - 1) * cos(t/2) with initial condition H(0) = 4.

Problem A: 00:26
Problem B: 01:16
Problem C: 10:00