How to determine when a function changes sign?

[hanson]

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?

 

[ice109]

i don't understand your notation, what does f(y:a) mean?

 

[tacman]

To determine when a function changes sign, you need to find the points where the function crosses the x-axis. In other words, you need to find the values of a where the function equals 0. This can be done by setting the function equal to 0 and solving for a. Once you have the values of a, you can plug them back into the function and see if the sign changes between 0 and 1+a.

In your specific example, you can set f(y;a) equal to 0 and solve for a. This will give you the values of a where the function changes sign. Then, you can plug those values back into the function and see if the sign changes between 0 and 1+a.

Another way to determine when a function changes sign is to graph it and look for where it crosses the x-axis. This can give you a visual representation of the points where the sign changes.

Overall, the key is to find the points where the function equals 0 and then test those points to see if the sign changes. I hope this helps!