etch the graph of y=x+(1/x). i got stuck for x=0. and i also want to find maxima and minima.

Question

Sketch the graph of y=x+(1/x). i got stuck for x=0. and i also want to find maxima and minima. please using graph show maxima and minima.?

here maxima <minima. why ??

Answer 1

Step 1:

The equation is .

Construct a table for different values of x :

 Note : The equation does not exist at , so is not considered in the above table.

Step 2:

Graph:

1. Draw a coordinate plane.

2. Plot the points found in tables and draw a smooth curves through these points.

Observe the graph :

The equation has a maximum at .

The equation has minimum at .

Step 3:

The maximum of the function :

has a relative or local maximum at , if  for every x in open interval around .

The minimum of the function :

has a relative or local minimum at , if  for every x in open interval around .

Therefore, from the above two definitions maximum is always less than the minimum.

Solution :

The graph of the function :

The equation has a maximum at .

The equation has minimum at .