Definition of Relative Extrema :

1. If there is an open interval containing  on which  is a maximum, then  is called a relative maximum of  or you can say that  has a relative maximum at .

2. If there is an open interval containing  on which  is a minimum, then  is called a relative minimum of  or you can say that  has a relative minimum at .

Definition of Global Extrema :

The minimum and maximum of a function on an interval are also called the absolute minimum and absolute maximum, or the global minimum and global maximum.

Now observe the graph :

The graph increasing over interval .    (approximately)

The graph is ideal for a short period .

Again the graph is increasing over the interval  .

So the function has critical number at .

But the function does not have maximum or minimum at .

The function has a critical number at .

The function does not have maximum or minimum at .