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]