Trying to derive this but has multiple absolute values

In summary, the conversation discusses the difficulty and techniques for deriving expressions that contain multiple absolute values. It mentions that absolute values can cause challenges in finding the correct solution and that special rules and computer programs can be used to simplify the process. Overall, the conversation highlights the importance of understanding absolute value functions in mathematical derivations.
  • #1
souldoutt
4
0

Homework Statement


Find the Local and absolute extrema of f(x) on the interval [-1,2] and give a sketch of the graph if:

f(x) = [ 1 / (1 + |x|) ] + [ 1 / (1 + |x - 1|) ]




I am confused about the absolute value parts. I know they're the versions inside the absolute value signs when >0 and the negative of the inside when < 0 but I'm not sure how to start this derivative.

Help would be appreciated. Thanks.
 
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  • #2
souldoutt said:
I know they're the versions inside the absolute value signs when >0 and the negative of the inside when < 0
If you can't study both cases together, then study each case separately.
 

What does it mean to "derive" something?

To "derive" something means to find the mathematical relationship or formula that describes it. In other words, it is the process of working backwards to figure out how a certain result was obtained.

What are "absolute values"?

Absolute values are a mathematical concept that represents the distance of a number from zero on a number line. They are always positive and can be thought of as the magnitude or size of a number, regardless of its sign.

Why is it difficult to derive something with multiple absolute values?

Deriving something with multiple absolute values can be challenging because it involves working with multiple equations and variables simultaneously. The absolute values can also create different cases or scenarios that need to be considered, making the problem more complex.

How can one go about deriving something with multiple absolute values?

The best approach to deriving something with multiple absolute values is to break the problem down into smaller, more manageable parts. This could involve simplifying the equations, considering different cases, or using algebraic techniques such as substitution or elimination.

What are some real-world applications of deriving something with multiple absolute values?

Deriving something with multiple absolute values is a common problem in mathematical modeling and can be applied to various fields such as physics, engineering, and economics. It can be used to analyze and understand complex systems, make predictions, and optimize solutions.

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