$\"\"$

The function is $\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Critical points of the function are the points where the first derivative is equals to zero.

Consider $\"\"$ .

$\"\"$ .

Apply deivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

Newton $\"\"$ s approximation method formula : $\"\"$ .

Substitute $\"\"$ and $\"\"$ .

$\"\"$ .

Perform Newton approximation for $\"\"$ .

The calculations for si iterations are shown in the table.

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Observe the table:

The critical point number is at $\"\"$ .

$\"\"$

Find the relative extrema, by substituting critical point in $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

The relative extrema is $\"\"$ .

Graph the functions $\"\"$ and $\"\"$ .

$\"\"$

Observe the graph:

The critical point number is at $\"\"$ .

The relative extrema is $\"\"$ .

$\"\"$

Graph:

Graph the functions $\"\"$ and $\"\"$ .

$\"\"$

The critical point number is at $\"\"$ .

The relative extrema is $\"\"$ .