Max/Min of Polynomial Functions

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Homework Help Overview

The discussion revolves around finding the maximum and minimum values of polynomial functions without using calculus or derivative tests. Participants explore alternative methods applicable to polynomial equations, particularly focusing on quadratics and the implications of zeroes and their multiplicities.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss completing the square for quadratics and inquire about the implications of knowing the zeroes and their multiplicities on determining extrema.

Discussion Status

The conversation is ongoing, with some participants providing insights into specific cases, such as the behavior of polynomials at zeroes and the role of multiplicity in identifying maxima and minima. There is no explicit consensus yet, as various interpretations and methods are being considered.

Contextual Notes

Participants are operating under the constraint of not using calculus or derivatives, which shapes the nature of the discussion and the methods being explored.

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Homework Statement


Does anyone know a possible equation or way to solve for the Max and Min of a Polynomial Function without Calculus or the Derivative test??


Homework Equations





The Attempt at a Solution

 
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I do if it's a quadratic. Complete the square. You can do similar tricks with some other special polynomials. Otherwise it's using derivatives.
 
What if you are given the zeroes and the multiplicity of the zeroes?
 
It will tell you that the maxs and mins that aren't at zero are between the zeros, but it won't tell you much more about them. If you have, for example, a double zero at a, (x-a)^2 is a factor of the polynomial and you can say x=a is a max or a min depending on the sign of the rest of the terms, that is true.
 
Last edited:
ooo alright thanks a lot!
 

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