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

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Homework Help Overview

The discussion revolves around finding local maxima and minima of the function 0.1x^3 - 3x within the domain of [-10,10]. The original poster expresses uncertainty about their ability to approach this problem given their current knowledge in Calculus I, specifically before learning about derivatives.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss potential methods for approximating local extrema, including using midpoints between roots and graphing the function. Questions about the applicability of limit notation and the definition of a derivative are also raised.

Discussion Status

The discussion is active, with participants exploring various approaches to the problem. Some suggest using graphical methods for approximation, while others hint at the possibility of using limit notation to derive insights about the function. There is no explicit consensus on a single method, and multiple interpretations of the problem are being considered.

Contextual Notes

Participants note that the function has three roots and question the linearity of the function in relation to finding maxima and minima. The original poster is seeking a thorough understanding despite their current limitations in calculus knowledge.

ktpr2
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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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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?
 
Can't u use a computer & graph it...?

Daniel.
 
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 <br /> and <br /> 0[/tex]
The midpoint isn't the max/min cause the function isn't linear (i think that's why).
 
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.
 
If you know limit notation I think you can cheat and use the definition of a derivative.
 

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