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Extreme Value Theorem Exercises

Example 1

Consider the function f(x) = 2cos(x) + 1 on the interval [-2π, 2π]:

• What is the maximum value of the function on this interval?

Example 2

Consider the function f(x) = 2cos(x) + 1 on the interval [-2π, 2π]:

• What are the values of x at which the maximum is attained?

Example 3

Consider the function f(x) = 2cos(x) + 1 on the interval [-2π, 2π]:

• What is the minimum value of the function f on this interval?

Example 4

Consider the function f(x) = 2cos(x) + 1 on the interval [-2π, 2π]:

• What are the values of x at which the minimum is attained?

Example 5

Let . On which of the following intervals can we use the Extreme Value Theorem to conclude that f must attain a maximum and minimum value on that interval?

• (0, π)
• (0, π]
• [0, π]
• (1, 2)
• (1, 2]
• [1, 2]