Applications of Derivatives - Rate of Change

Grade 12 Maths — Applications of Derivatives - Rate of Change: 25 practice questions with instant scoring and explanations.

1. The average rate of change of f(x) over [a, b] is:
2. The instantaneous rate of change of f at x = a is:
3. If position s(t) = t² + 3t, then velocity at t = 2 is:
4. Acceleration is defined as:
5. If the position function is s(t) = 5t³ − 2t, then acceleration at t = 1 is:
6. The derivative dy/dx represents:
7. If the radius of a circle is increasing at 2 cm/s, the rate of change of area when r = 5 is:
8. The related rates method is used to find:
9. If water is poured into a cone at 10 cm³/s, dV/dt equals:
10. The marginal cost in economics is:
11. If C(x) = 5x² + 10x + 100 is the cost function, marginal cost at x = 20 is:
12. The rate of change of velocity is called:
13. If a ball is thrown upward with initial velocity 30 m/s, its velocity after 2 seconds is (g = 10 m/s²):
14. For a pendulum oscillating, the displacement y = 5 sin(2t). The velocity at t = π/4 is:
15. The rate of change of population P(t) at time t is:
16. If V = (4/3)πr³, then dV/dr at r = 2 is:
17. The profit function is P(x) = R(x) − C(x). The marginal profit is:
18. If the area A = 6xy and x increases at 2 units/s while y decreases at 1 unit/s, then dA/dt in terms of x and y is:
19. Angular velocity ω is the rate of change of:
20. If a ladder of length 10 m leans against a wall and the base moves away at 3 m/s, the rate at which the top moves down when the base is 6 m away is:
21. The average value of a function on [a, b] is:
22. Elasticity of demand is:
23. If the temperature T(t) = 20 + 10e^(−0.5t), the rate of change at t = 0 is:
24. Question?
25. Question?