When Should You Use Derivatives?

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Discussion Overview

The discussion centers on understanding when to use derivatives in various contexts, including theoretical applications, real-life scenarios, and practical measurements. Participants explore the relevance of derivatives in both mathematical problems and everyday situations.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the criteria for using derivatives, suggesting a need for guidance on their application.
  • Another participant identifies clear instances where derivatives are necessary, such as finding maximum/minimum points and related rates.
  • A participant emphasizes the importance of derivatives in real-life applications, particularly in technical fields requiring precise measurements.
  • It is noted that derivatives are frequently encountered in physics, particularly in measuring rates of change like velocity and acceleration.
  • One participant poses a question about deriving equations related to walking, indicating a desire for practical examples of derivative application.
  • A flowchart is suggested to help determine when to use derivatives based on whether quantities change with time or space.
  • Another participant discusses the practicality of measuring speed directly versus calculating it from distance, highlighting that the choice depends on the context and available measurements.
  • A participant expresses gratitude for the insights shared, indicating a growing understanding of when to apply derivatives.

Areas of Agreement / Disagreement

Participants express a range of views on the application of derivatives, with some agreeing on their necessity in technical contexts while others highlight practical considerations. The discussion remains unresolved regarding the best approach to determine when derivatives should be used.

Contextual Notes

The discussion reflects varying levels of familiarity with derivatives and their applications, with some participants seeking clarity on practical usage while others provide examples and reasoning based on their experiences.

thharrimw
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when to use derivatives??

i have taught myself all the different ways to find derivatives that were in a old college textbook so I was wondering if anyone could tell me how you know when you need to use derivatives.
 
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Not really sure how to answer this.

Obvious reasons: when the problem asks you to, if you're trying to find the max/min/inflection points of a function, related rates?
 
i mean in real life uses for derivatives.
 
Well, think about what derivatives are. The derivative of a function is the rate of change at a specific point rather than 'average rate of change'. You do NOT need derivatives if your "real life" consists of saying "do you want fries with that" but any sort of technical work that requires precise answers (an exact value rather than an approximation or an average) uses the derivative.
 
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If physics is "real life" enough for you, you need them all the time. As HallsOfIvy said, derivatives measure rates of change. Commonly encountered in everyday life are rate of change of position (a.k.a. velocity), velocity (a.k.a. acceleration), temperature, and about any other physical quantity you can think of.
Also if you have any model which involves rates of change in time, you will encounter derivatives, whether it be water height of the sea, air flow through a tube or stock rates.
 
ok but how do you get the equations of someone walking.
 
Here's a flowchart for you:

Is the quantity you're interested in changing with time and/or with space?
Yes? "Use Derivatives"
No? Then why are you interested in it?
 
Last edited:
… it all depends …

thharrimw said:
ok but how do you get the equations of someone walking.

Hi thharrimw! :smile:

I suspect that what's worrying you is why would you. for example, want to find the derivative of the distance when you could easily measure the speed directly?

And the answer is … in practice, it just depends what is easiest to measure!

If someone is walking, or driving, and you want to know their speed … well, you just measure it by using a radar gun, or looking at the speedometer, or …

In that case, it would be really silly to measure the distance, and do a calculation.

But sometimes you aren't able to measure the speed directly.

For example. you might want to know how fast a tank of water is emptying, but your only measurement is of the height of a float on the top. Then you'd have feed the measurements into a computer, which would find the derivative for you. (Or you could just plot the heights on a graph, and measure the slope!)

It all depends … :smile:
 
thanks tiny-tim that helps a lot becouse i know how to find derivatives but i am just starting to learn where you should use them
 

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