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

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To find the local maxima and minima of the function 0.1x^3 - 3x within the domain of [-10,10], the discussion highlights the use of limit notation and the concept of derivatives, which the user is just beginning to learn. While the user considers using the midpoint between roots to approximate these values, it is noted that this method may not yield accurate results due to the non-linear nature of the function. The function has three roots, and plotting the function can help visualize the extrema. The suggestion is made that using the definition of a derivative could provide a more precise approach. Overall, the discussion emphasizes the importance of calculus concepts in accurately determining local maxima and minima.
ktpr2
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Hi,

I have the function 0.1x^3 - 3x 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
\sqrt{1.2}/1.2 <br /> and <br /> 0
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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