Question

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

Answer 1

Step 1 :  

The expression is and the point is .

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

Let .

Apply derivative on each side with respect to x. 

Apply quotient rule of derivatives :

Step 2 :

Slope at the point :

Substitute  in  

The slope is .

Step 3 :

Point-slope form of line equation .

Substitute point and slope in the above equation.

 

Tangent line equation is 

Solution : 

Tangent line equation is