TOAN !

Open Ended

What is the significance of understanding the behavior of functions and their derivatives in real-world applications?

Multiple Choice

Một chất điểm chuyển động với vận tốc được cho bởi công thức v(t) = -3t^2 + 12t + 1 với t (giây) là khoảng thời gian tính từ khi bắt đầu chuyển động. Hỏi sau bao lâu khi chất điểm chuyển động thì đạt được vận tốc lớn nhất?

• 2(s)

• 1(s)

• 13(s)

• 4(s)

Multiple Choice

Cho hàm số y = f(x) xác định với mọi x ≠ -4 có bảng biến thiên như hình dưới đây. Hàm số biến trên khoảng nào trong các khoảng sau?

• (-7;+∞)

• (-7;-4)

• (6;+∞)

• (-7;4)

Multiple Choice

Given the function y = f(x) with the graph of its derivative y = f'(x) as shown, on which interval is the function increasing?

• (0;1)

• (-∞;1)

• (-1;1)

• (1;4)

Multiple Choice

What are the critical points of the function y = f(x) = x^3 - 21/2 x^2 + 36x - 1?

• x = 8

• x = 4

• x = 1

• x = 3

Multiple Select

Which of the following statements about the function y = x^3 - 3x^2 - 9x + 35 is correct?

• The function is decreasing on the interval (-1;3).

• f'(x0) > 0 for all x0 in (3;+∞).

• The function attains a local maximum at x = 3.

• The maximum value of the function on [-4;4] is 40.

Multiple Choice

What is the minimum value of the function y = 2x^2 - 2x + 2 at x = 1?

• 6

• -2

• 0

• 2

Multiple Choice

f'(x) is pictured. Which x values does f(x) has a relative min?

• x=-5 and -1

• x=-3

• x=-1

• x=-5

Open Ended

After this session on functions and their applications, do you have any questions or topics you would like to explore further?

Multiple Choice

f'(x) is pictured. Which x values does f(x) has a relative max?

• x=-5 and -1

• x=-3

• x=-1

• x=-5

Multiple Choice

A person wants to row from point A to point B along a river. If the river flows at a speed of 3 km/h, and the person rows at a speed of 6 km/h, what is the total time taken to row from A to B if the distance from A to B is 8 km?

• 1 hour

• 2 hours

• 3 hours

• 4 hours

Multiple Choice

Given the graph of f '(x), f(x) has ...

• a local min at x = -6

• a local min at x = 2

• a local min at x = 2 and

  a local max at x = -6

• local mins at x = -2, 5 and

  a local max at x = 3

Open Ended

Calculate the value of a + b + c for the function y = x³ + ax² + bx + c given the critical point A(-1;29) and passing through point B(2;2).

Multiple Choice

Given the sign chart for f '(x), f(x) has ...

• a local maximum at x = -2.

• a local minimum at x = -2 and

  a local maximum at x = 4.

• a local maximum at x = -2 and

  a local minimum at x = 4.

• no extrema.

Multiple Choice

What is the maximum volume of the box formed with a base area of 5.5 m² and a height h(m) when the width is x(m)?

• 1.17 m³

• 2.5 m³

• 3.0 m³

• 4.0 m³

Multiple Choice

Find all values of m such that the function y = x^3 - 3x^2 + (5 - m)x is defined on the interval (2; +∞).

• m ≤ 5

• m > 5

• m < 2

• m = 0

Poll

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