Question

Find all points (x,y) on the graph of y = x/(x - 2) with tangent lines perpendicular to the line y = 2x+3.
Help.

Answer 1

slope of graph=-2/(x-2)^2

Answer 2

equate it to perpendicular slope of line given
that is -1/2

Answer 3

then (x-2)^2=4
x=6or-2

Answer 4

hence our required points are
(6,3/2) (-2,1/2)