Definition of local maximum and local minimum :

1. The number is a local maximum value of  if when is near .

2.The number is a local minimum value of if when is near .

Definition of absolute maximum and absolute minimum :

Let be a number in the domain of a function .

1.The number is a absolute maximum value of  on  if for all in .

2.The number is a absolute minimum value of on  if for all in .

The function is , .

Construct a table for different values of :

Graph :

1) Draw the co-ordinate plane.

2) Plot the points.

3) Connect the points with a smooth curve.

Observe the graph.

There is no absolute maximum, because the highest part of the graph is

leads to a hole.

There is no absolute minimum, because the lowest part of the graph is

leads to a hole.

Hence, the function has no extrema.

Graph of the function is

No extreme points.