The problem involves finding the value of k such that the line y - 36x = k is a normal to the curve defined by y = 1 / abs(x-2). The discussion centers around the implications of the absolute value in the context of the curve's behavior and its derivatives.
The discussion is ongoing, with participants exploring the graphical representation of the absolute value function and its derivatives. There is an acknowledgment of the need to understand the behavior of the curve before proceeding with algebraic methods.
Participants note that the behavior of the curve changes at x = 2, which is relevant for determining the sign of the absolute value term. There is a focus on the derivative's sign in relation to the curve's characteristics.
Have you drawn a graph of the absolute value function?Kqwert said: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?
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 said:Have you drawn a graph of the absolute value function?
Kqwert said: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...?