How to determine when a function changes sign?

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SUMMARY

The discussion focuses on determining the conditions under which the algebraic function f(y; a) = y^4 + b*y^3 + c*y^2 + d*y + e changes sign between the intervals 0 and 1+a. The coefficients b, c, d, and e are dependent on the parameter a. Participants are seeking clarification on the notation used and how to analyze the function's behavior within the specified range.

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  • Knowledge of sign changes in mathematical functions
  • Basic calculus concepts, particularly related to function behavior
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hanson
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Hi all.
Say, I have an alegebric function, e.g. f(y;a)=y^4+b*y^3+c*y^2+d*y+e,
where the coefficients b,c,d and e are all depends on a single parameter, a.

What I want to do is to check what is the condition of a for the function f(y;a) to change its sign between 0 and 1+a, do you have any idea to do so?
 
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i don't understand your notation, what does f(y:a) mean?
 

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