Step 1:

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

Differentiate the function with respect to $\"\"$ .

$\"\"$

Power rule of derivatives : $\"\"$ .

$\"\"$

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

This is the slope of the tangent line.

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

Step 2 :

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

Substitute $\"\"$ and $\"\"$ in the above equation.

$\"\"$

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

Step 3:

Use the linear approximation to complete the table.

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

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

Notice that the closer x is to 2, the better the approximation is.

The linear approximation $\"\"$ depends on the point of tangency.

At the different point on the graph of $\"\"$ , obtain a different tangent line approximation.

The graph is :

$\"\"$