$\"\"$

The function is $\"\"$ and the point is $\"\"$ .

$\"\"$

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

$\"\"$

$\"\"$ .

At the point $\"\"$ , $\"\"$ .

This is the slope of the tangent line.

Slope of the tangent line is $\"\"$ .

$\"\"$

Point-slope form of the line equation is $\"\"$ , where $\"\"$ is slope.

Substitute $\"\"$ and $\"\"$ in point-slope form.

$\"\"$

The tangent line equation is $\"\"$ .

$\"\"$

Use the linear approximation to complete the table.

\ \

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

The table compares the values of $\"\"$ given by linear approximation with the values of

$\"\"$ near $\"\"$ and $\"\"$ .

$\"\"$

The tangent line equation is $\"\"$ .

The completed table :

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