Find max/min within what we've been taught?

  • Thread starter ktpr2
  • Start date
In summary, the speaker is trying to find the local maxima and minima of the function 0.1x^3 - 3x within the domain of [-10,10]. They are currently in Calculus I and just before learning about derivatives. They are wondering if there is a way to find the fraction representing the max and min using their current knowledge and if limit notation can be used to approximate the values. They mention having roots at \sqrt{1.2}/1.2 and 0 and note that the midpoint between these roots is not the max or min. They also mention that the function has 3 roots. Another speaker suggests using limit notation to cheat and find the values using the definition of a derivative.
  • #1
ktpr2
192
0
Hi,

I have the function [tex] 0.1x^3 - 3x[/tex] and I would like to find its local maxima and minima within the domain of [-10,10]. The problem is I don't think we've been taught a way yet; I'm currently in Calculus I and just before derivatives. Is there a way within my current knowledge to find the fraction representing the max and min of this function within the above domain?
 
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  • #2
I would think that the local max and min could be approximated by taking the midpoint x value between roots. Edit: Have you been taught limit notation yet?
 
  • #3
Can't u use a computer & graph it...?

Daniel.
 
  • #4
Yeah we've been taught limit notation. And we can probably just give the value 3.1622... but I'm trying to be as thorough as possible.

We have roots
[tex]\sqrt{1.2}/1.2
and
0[/tex]
The midpoint isn't the max/min cause the function isn't linear (i think that's why).
 
  • #5
Unfortunately u can find the exact (x,y) values or the extrem through calculus.Approximate values can be achived by plotting...It has 3 roots,BTW

Daniel.
 
  • #6
If you know limit notation I think you can cheat and use the definition of a derivative.
 

1. What is the purpose of finding max/min within what we've been taught?

The purpose of finding the maximum and minimum values within what we've been taught is to identify the highest and lowest points within a given set of data or information. This can help us understand the range and variability of the data, and make informed decisions based on the extremes.

2. How do we find the max/min within what we've been taught?

The process of finding the maximum and minimum values within what we've been taught depends on the specific data or information we are working with. However, some common methods include graphing the data and visually identifying the highest and lowest points, using mathematical equations or algorithms, or using built-in functions in software or programming languages.

3. What factors should we consider when finding max/min within what we've been taught?

When finding the maximum and minimum values within what we've been taught, it is important to consider the context of the data and the purpose of the analysis. Factors such as the type of data (numerical, categorical, etc.), the size of the data set, and the distribution of the data can all affect the approach and interpretation of the results.

4. Can we find multiple max/min values within what we've been taught?

Yes, it is possible to find multiple maximum and minimum values within what we've been taught. This can occur when there are multiple peaks or valleys in the data, or when there are ties for the highest or lowest values. In these cases, it is important to consider the context of the data and the purpose of the analysis to determine the most relevant maximum or minimum values.

5. How can finding max/min within what we've been taught be useful?

Finding the maximum and minimum values within what we've been taught can be useful in various ways. It can help us identify outliers or extreme values that may impact the overall interpretation of the data, understand the variability or range of the data, and make informed decisions based on the extremes. It can also be used to compare different sets of data or track changes over time.

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