Derivation, absolute value problem

[Kqwert]

Homework Statement

Find k so that y - 36x = k is a normal to the curve y = 1 / abs(x-2).

Homework Equations

The Attempt at a Solution

My problem is regarding the absolute value. I know that the tangent to the curve must be (-1/36). In the solutions manual, it is said that by knowing the sign of the tangent (i.e. negative) we can know the sign of the absolute value term. How is this possible?

 

[PeroK]

Homework Statement

Find k so that y - 36x = k is a normal to the curve y = 1 / abs(x-2).

Homework Equations

The Attempt at a Solution

My problem is regarding the absolute value. I know that the tangent to the curve must be (-1/36). In the solutions manual, it is said that by knowing the sign of the tangent (i.e. negative) we can know the sign of the absolute value term. How is this possible?

Have you drawn a graph of the absolute value function?

 

[Kqwert]

Have you drawn a graph of the absolute value function?

Yes I have, but not sure exactly what I know by doing that. Or, I guess I can see that x must be larger than 2, because that is the only place of the curve where it has a negative derivative? And therefore I know that the absolute value sign is positive...?

 

[PeroK]

Yes I have, but not sure exactly what I know by doing that. Or, I guess I can see that x must be larger than 2, because that is the only place of the curve where it has a negative derivative? And therefore I know that the absolute value sign is positive...?

I think that's the idea. You can see from the graph before you start any algebra what solution approx you are looking for.