Find an equation of the tangent line to the graph of f at the given point

Question

(a) Find an equation of the tangent line to the graph of f at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of a graphing utility to confirm your results.

Answer 1

Step 1:

(a)

The function is .

The slope of the tangent line is equal to the derivative of the function at .

Apply derivative on each side.

                        

   

          

Step 2:

Slope at the point , Substitute in .

Answer 2

Contd...

Step 3:

Use point-slope form of equation .

Substitute point and slope in the above equation.

Step 4:

(b)

Graph the function   and tangent line  in same viewing window.

Answer 3

Contd...

Step 5:

Now verify the result using the derivative feature of the graphing utility.

Solution:

(a) The tangent line is .

(b)

(c)