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Find an equation of the tangent line to the graph of the function at the given point. (x+1/x-1)^2 (3,4)?

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Find an equation of the tangent line to the graph of the function at the given point. (x+1/x-1)^2 (3,4)?
asked Feb 9, 2015 in CALCULUS by anonymous

1 Answer

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Step 1 :  

The expression is image and the point is image.

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

Let image.

Apply derivative on each side with respect to x

image

Apply quotient rule of derivatives : image

image

image

Step 2 :

Slope at the point image :

Substitute image in image 

image

The slope is image.

Step 3 :

Point-slope form of line equation .

Substitute point image and slope image in the above equation.

image 

Tangent line equation is image

Solution : 

Tangent line equation is image

answered Feb 9, 2015 by Thomas Apprentice

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