1. A particle moves along a straight line, and its position at time t is given by s(t) = 3t^2 – 2t + 1. What is the velocity of the particle at time t = 2?

2. A rectangular box with a square base is increasing its volume at a rate of 100 cubic units per minute. If the length of an edge of the base is x, and the height is h, find the rate at which the height is changing when x = 4.

3. The cost in dollars of producing x units of a product is given by C(x) = 0.5x^3 – 2x^2 + 100x + 200. Find the marginal cost when x = 10.

4. The height of a triangle is increasing at a rate of 2 cm/min, while the base is decreasing at a rate of 3 cm/min. If the height is 5 cm and the base is 10 cm when the height is increasing, find the rate at which the area of the triangle is changing.

5. The radius of a circle is increasing at a rate of 2 cm/s. Find the rate at which the area of the circle is changing when the radius is 5 cm.

6. A rectangular tank with a square base is being filled with water at a rate of 10 cubic feet per minute. If the tank is 4 feet tall and the base has sides of length 2 feet, find the rate at which the height of the water is changing when the depth is 3 feet.

7. A company’s revenue function is given by R(x) = 5x^2 + 20x, where x represents the quantity of a product sold. What is the marginal revenue when x = 3?