How do you find the equation of a line tangent to #y=4/x# at (2,2)?

1 Answer
Aug 24, 2016

We know that the tangent passes through the point #(2,2)#, so we only need to find out the slope of the tangent at that point.

Explanation:

But the slope of the tangent of #y# at a given point is the value of the first derivative at that point. Now, for this function:

#y'=-4/x^2#, and so evaluating at #x=2# we get

#y'(2)=-4/(2^2)=-1#

Then we now know that the tangent is #y=(-1)*x+b#, and since the point #(2, 2)# is on the line we also know that:

#2=(-1)*2+b#. Then #b=4# and the equation of the tangent is:

#y=-x+4#