derivative quiz

Question

find where (what are the coordinates) the tangent line to the graph of f(x)=(x+1)/(x-1) is parallel to the line whose equation is 2y+x=6

Answer 1

2y + x = 6

y =-x/2 + 3

slope =-1/2

y = (x+1)/(x-1)

y= [(x-1) - (x+1)]/(x-1)^2 = -1/2

=-2/(x-1)^2 = -1/2

(x-1)^2 =4

x-1 = + or - 2

x= -1 or 3

y= 0 or 2

the points of tangency with the same slope as the line are (-1,0) and (3,2)

the tangent line are y=-x/2 + b. calculate b by plugging in the points

0=-1/2 + b, b = 1/2

on tangent line is y=-x/2 + 1/2

2 =-3/2 + b

b = 2+3/2 =7/2

the other tangent line is y=-x/2 +7/2