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]

Answer

- (0,π) - We cannot use the Extreme Value Theorem because this interval is not closed.

- (0,π] - We cannot use the Extreme Value Theorem because this interval is not closed.

- [0,π] - We cannot use the Extreme Value Theorem because
*f* is discontinuous at x = 0, and therefore *f* is not continuous on this interval.

- (1,2) - We cannot use the Extreme Value Theorem because this interval is not closed.

- (1,2] - We cannot use the Extreme Value Theorem because this interval is not closed.

- [1,2] - We can use the Extreme Value Theorem because this interval is closed and
*f* is continuous on this interval.