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...?
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.
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.
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.
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.
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.