Functions and Derivatives

Can you conclude anything about the extreme values of a continuous function on an open interval? On a half-open interval? Give reasons for your answer.

Step 1 of 3 :

In this problem, we have to give conclusion about the extreme values of a continuous function on an open interval.

Step 2 of 3 :

Continuous function defined over an open interval or an half- open interval need not have any of the absolute extreme values.

Example:

(i)

Let be a function defined over

is continuous over

Both the absolute extreme values will not be at the end of an open interval.

(ii)

achieve both global min (-1) and global max (1) inside the open or half open interval.

have neither a global min nor a global max inside the open or half-open interval.