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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 the graphing utility to confirm your results.

Function                                    point

y = (4x3+ 3)2                             (-1, 1)

asked Jan 22, 2015 in CALCULUS by anonymous

3 Answers

0 votes

Step 1:

(a)

The function is .

Apply derivative on each side

Apply chain rule of derivative image.

Step 2:

slope at the point , Substitute x = -1  in .

image

Find the tangent line equation using point-slope form .

image

image

The tangent line equation is image.

 

answered Jan 22, 2015 by yamin_math Mentor
edited Jan 22, 2015 by yamin_math
0 votes

Step 3:

(b)

Graph the function and tangent line image to verify the result.

image

Step 4:

(c)

Verify the derivative of the function using graphing utility .

image

So , the derivative of the function verified graphically.

The derivative of the function is .

 

answered Jan 22, 2015 by yamin_math Mentor
0 votes

Solution :

(a) The tangent line equation is  image.

(b)

Graph of the function and tangent line image.

image

(c)

The derivative of the function is .

image

answered Jan 22, 2015 by yamin_math Mentor

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