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

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(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.

asked Jan 29, 2015 in CALCULUS by anonymous

3 Answers

0 votes

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 image in image.

image

answered Jan 29, 2015 by yamin_math Mentor
edited Jan 29, 2015 by yamin_math
0 votes

Contd...

Step 3:

image

Use point-slope form of equation .

Substitute point image and slope image in the above equation.

image

Step 4:

(b)

Graph the function   and tangent line image in same viewing window.

image

answered Jan 29, 2015 by yamin_math Mentor
0 votes

Contd...

Step 5:

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

image

Solution:

(a) The tangent line is image .

(b)

image

(c)

image

answered Jan 29, 2015 by yamin_math Mentor

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