Question
Find the equation of each tangent line to the curve y=(1/x) that has a slope of -1. Find each point of tangency.
Answers
Reiny
if y = 1/x
then y' = -1/x^2
given , y' = -1
-1/x^2= - 1
x^2 = 1
x = ± 1
find the corresponding y values.
You have 2 tangents, one at (1,1) , the other at (-1,-1)
Use your favourite method to find the equation of those tangents.
(The question is poorly worded when it asked for the equation of the tangent, implying there is only one)
then y' = -1/x^2
given , y' = -1
-1/x^2= - 1
x^2 = 1
x = ± 1
find the corresponding y values.
You have 2 tangents, one at (1,1) , the other at (-1,-1)
Use your favourite method to find the equation of those tangents.
(The question is poorly worded when it asked for the equation of the tangent, implying there is only one)