ỨNG DỤNG ĐẠO HÀM ...

Multiple Choice

Which of the following is an example of an optimization problem in daily life?

• Finding the shortest route to school

• Memorizing a poem

• Painting a picture

• Reading a novel

Open Ended

Why is it important to understand the rate of change of a quantity in real-life situations?

Multiple Choice

What is the maximum number of spectators that a football stadium can hold according to the scenario described?

• 27,000

• 55,000

• 30,000

• 100,000

Open Ended

Explain how the concept of instantaneous rate of change is defined mathematically for a function y = f(x).

Multiple Select

Which of the following are applications of the instantaneous rate of change in real life?

• Calculating the speed of a moving object at a specific time

• Finding the average cost of production

• Determining the rate of a chemical reaction at a given moment

• Measuring the total population over a period

Multiple Choice

In the example of the yeast population, what is the long-term maximum number of yeast cells according to the model?

• 20

• 25

• 100

• 200

Open Ended

Compare the marginal cost C'(200) with the cost of producing the 201st unit of goods in the given economic example. What conclusion can you draw?

Open Ended

Explain why it is not possible to remove 100% of air pollutants from factory emissions based on the given cost function.

Multiple Choice

Which of the following best describes the behavior of the cost function C(x) as x approaches 100 in the context of removing air pollutants from factory emissions?

• The cost decreases to zero.

• The cost remains constant.

• The cost increases without bound.

• The cost oscillates.

Open Ended

Explain the process of finding the price that maximizes revenue in the stadium ticket sales scenario. What mathematical steps are involved?

Multiple Choice

What is the optimal ticket price to maximize revenue according to the stadium ticket sales problem?

• 100 thousand VND

• 90 thousand VND

• 95 thousand VND

• 85 thousand VND

Multiple Choice

According to the profit function for the blender company, what is the minimum number of blenders that must be produced each month to break even?

• 0

• 20

• 100

• 200

Open Ended

If a company wants to maximize profit from TV sales, what price should they set for each TV and how many TVs should they aim to sell? Justify your answer using the given functions.

Multiple Select

Which of the following are steps to determine the optimal price for maximizing TV sales revenue, as shown in the example?

• Find the demand function p(x)

• Find the revenue function R(p)

• Set the derivative of revenue to zero

• Calculate the cost function

Multiple Choice

Given the velocity function v(t) = 3t^2 - 12, for what interval of t does the particle move upward?

• 0 ≤ t < 2

• t > 2

• t = 2

• t < 0

Open Ended

Explain the significance of the marginal cost at x = 100 in the context of the cost function C(x).

Multiple Choice

Which of the following statements about the revenue function R(p) in the apartment rental problem is correct?

• The revenue is maximized when p = 8.

• The revenue is maximized when p = 9.

• The revenue is maximized when p = 10.

• The revenue is maximized when p = 8.1.

Open Ended

After learning about the application of derivatives to solve real-world problems, what is one question you still have or a topic you would like to explore further?

Multiple Choice

What are the two main topics covered in this lesson about the application of derivatives to real-world problems?

• The rate of change of a quantity and some simple optimization problems

• The history of derivatives and famous mathematicians

• The definition of a function and its properties

• The use of integrals in physics