Differential Calculus

Problem
A Toyota Land Cruiser drives east from point A at 30 kph. Another car, Ford Expedition, starting from B at the same time, drives S30°W toward A at 60 kph. B is 30 km from A. How fast in kph is the distance between two cars changing after 30 minutes? Hint: Use the Cosine Law.

Problem
Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t.

Problem
A parabola has an equation of y² = 8x. Find the equation of the diameter of the parabola, which bisect chords parallel to the line x – y = 4.

Problem
A point moves in the plane according to equations x = t² + 2t and y = 2t³ - 6t. Find dy/dx when t = 0, 2, 5.