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Continuity of Functions

Continuity of Functions

Example 1

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

  • What is the maximum value of the function f 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]
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