I'm Software engineer and I'm having little issue solving this problem let's called H.
Well I'm looking for the mathematical expression of the function f(x) based on 3 equations and one inequality. f(x) passes through 3 points and f(x) is a decreasing function when X€[0,END]
H = {f(0)=1, f(t)=α, f(50400)=0, f '(x)<0} and 0< t < END=50400, 0< a <1.
what i tried: I supposed the solution is polynomial of order 3 and can be expressed this way:
f(x)= ax(x-t)(x-END) + bx(x-t)+ cx+ d
I found d,c,b still a !
- Q1: Well am I doing this right ?
- Q2: is there any theory I can use to find the solution ?
EDIT 1:
I know this have infinit solution so a solution with a lesser degree is preferable.