Untitled Presentation

Multiple Choice

For the function y = f(x) defined and continuous on [-3;5] with the given graph, what is the greatest value of y = f(x) on the interval [-3;5]?

• 3

• 5

• -3

• 2

Multiple Choice

What is the largest value of the function f(x) = x^3 - 3x^2 - 9x + 10 on the interval [-2;2]?

• -12.

• 10.

• 15.

• -2.

Multiple Choice

Given the variation table of the function y = f(x) on the interval [-1;3] as shown, which statement is correct?

• min f(x) = -1.

• min f(x) = 1.

• max f(x) = 5.

• max f(x) = 4.

Multiple Choice

Given the variation table of the function y = f(x) on the interval [0;3] as shown, what is the smallest value of the function on [0;3]?

• -4.

• 1.

• 4.

• 0.

Multiple Choice

Given the graph of the function f(x) as shown, what is the largest value of the function on the interval (-∞; -1)?

• 1.

• 2.

• -6.

• -3.

Multiple Choice

Given the graph of y = f(x) continuous on [-1;3], what is the value of M + m, where M and m are the maximum and minimum values of the function on the interval?

• -5

• 2

• -6

• -2

Multiple Choice

What is the maximum value of the function f(x) = x^3 + 3x - 6 on the interval [1;3]?

• 30

• 39

• 36

• 10

Multiple Choice

Find the minimum value of the function y = -x + 3 - 1/(x+2) on the interval (-4;-2).

• min y = 5

• min y = 4

• min y = 7

• min y = 15/2

Open Ended

Explain how to determine the maximum and minimum values of a continuous function on a closed interval using its graph.

Multiple Choice

On the interval [1;5], at which point does the function y = f(x) (as shown in the graph) attain its maximum value?

• x = 4

• x = 1

• x = 2

• x = 5

Multiple Choice

Which of the following statements is correct about the function y = f(x) with the given sign chart for f'(x)?

• min_{(-2;+∞)} f(x) = f(1)

• min_{(-∞;-3)} f(x) = f(-3)

• min_{(-2;1)} f(x) = f(1)

• min_{[-3;-2]} f(x) = f(-2)

Multiple Choice

What is the value of the expression represented by the area under the curve from x = -2 to x = 2 in the given graph?

• -6

• -2

• -5

• 2

Multiple Choice

Given the graph of the function y = f(x) on the interval [-3;5], what is the value of 2M - m, where M is the maximum and m is the minimum value of the function on this interval?

• 5

• 8

• 2

• 6

Multiple Choice

What is the maximum value of the function y = x^3 + 3x^2 - 9x - 6 on the interval [-1;2]?

• 7

• 5

• -11

• 21

Multiple Choice

Given the table of variations for the function y = f(x) on the interval [-4;3], which of the following statements is correct?

• min f(x) = -1 at x = 3

• max f(x) = 4 at x = -4

• max f(x) = 2 at x = 0

• min f(x) = -2 at x = 2

Multiple Choice

What is the minimum value of the function y = f(x) on the interval [0;3] given the table of variations?

• -4

• 1

• 4

• 0

Open Ended

After working through these examples, do you have any questions or topics related to finding extrema of functions from graphs or tables that you would like to explore further?

Open Ended

Reflecting on the problems about finding the maximum and minimum values of functions from their graphs and variation tables, what strategies did you find most helpful in solving these types of questions?