General Applied Calculus Quiz

1. What is the velocity of an object with position s(t) = 4t² - 3t + 2 at t = 2 s?

a) 13 m/s

b) 8 m/s

c) 16 m/s

d) 4 m/s

2. What is the acceleration for v(t) = 3t² - 6t + 5 at t = 1 s?

a) 0 m/s²

b) 6 m/s²

c) 3 m/s²

d) -6 m/s²

3. True or False: Velocity is the derivative of position.

a) True

b) False

4. What is the total distance traveled from t = 0 to t = 2 for v(t) = t - 1 m/s?

a) 0 m

b) 2 m

c) 1 m

d) 4 m

5. For an area A(x) = 2x² + 3x, what is the rate of change at x = 2?

a) 11 units²/unit

b) 8 units²/unit

c) 4 units²/unit

d) 14 units²/unit

6. What is the work done by a force F(x) = 5x N from x = 0 to x = 3 m?

a) 22.5 J

b) 15 J

c) 45 J

d) 5 J

7. For a cost function C(x) = x³ - 6x² + 15x, where is the minimum cost?

a) x = 2 units

b) x = 3 units

c) x = 0 units

d) x = 6 units

8. True or False: Optimization problems use derivatives to find extrema.

a) True

b) False

9. What is the rate of fluid flow Q(t) = 2t + 1 L/s at t = 4 s?

a) 2 L/s²

b) 9 L/s²

c) 4 L/s²

d) 1 L/s²

10. For a population density p(x) = 100e^(-0.2x) people/km², what is dp/dx at x = 1 km?

a) -20e^(-0.2) people/km³

b) 20e^(-0.2) people/km³

c) -100 people/km³

d) 0 people/km³