Question

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

Answer 1

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`