Derivation, absolute value problem

In summary, the conversation is about finding the value of k in the equation y - 36x = k so that it is a normal to the curve y = 1/abs(x-2). The discussion includes using the graph of the absolute value function to determine the sign of the absolute value term and how it relates to the negative derivative of the curve at x > 2.
  • #1
Kqwert
160
3

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?
 
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  • #2
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?
Have you drawn a graph of the absolute value function?
 
  • #3
PeroK said:
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...?
 
  • #4
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...?

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

Related to Derivation, absolute value problem

1. What is a derivation?

A derivation is a mathematical process of finding the rate of change of a function with respect to one of its variables. It is a fundamental concept in calculus and is used to solve problems involving motion, growth, and optimization.

2. How do you solve an absolute value problem using derivation?

To solve an absolute value problem using derivation, you first need to rewrite the absolute value expression as a piecewise function. Then, you can use the definition of a derivative to find the derivative of each piece and determine the critical points. Finally, you can use the first or second derivative test to determine the maximum or minimum values of the function.

3. What are the applications of derivation in real life?

Derivation has many applications in real life, such as predicting the motion of objects, determining the maximum or minimum values of a function, and finding the best solution for optimization problems. It is also used in economics, physics, engineering, and other fields.

4. Can you explain the chain rule in derivation?

The chain rule is a formula used to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. It is an essential tool in solving more complex derivation problems.

5. Is derivation only used in calculus?

Derivation is primarily used in calculus, but it also has applications in other areas of mathematics, such as differential equations, linear algebra, and multivariable calculus. It is a fundamental concept in many mathematical fields and is often used in solving real-world problems.

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