Calc Extreme Value Theorum

Question

2. Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval [0,2π]?

a. y= 1/(1 + sinx)

b. y= 1/(x² + π)

c. y= x² - 2πx + π²/(x - π)

d. y= |x - π|/x - π

Answer 1

Only one of these functions is continuous on the stated interval and that is #b.

The theorem referenced applies only to continuous functions

All of the others have points where the function becomes unbounded.