Finding equation of a curve

[davidmandis]

Hi,
I need to find a single equation to represent the curve shown in the attached figure. I have access to MATLAB if that will help. Can anyone help me out?

Thanks,
David

[HallsofIvy]

What exactly do you mean by "a single equation"? That can be simply written as a "piecewise linear function": f(x)= x/2000 if x\le 4000, f(x)= 2 if x> 4000.

If you want a "single expression", use the Heaviside function H(x) which is defined by "H(x)= 0 if x\le 0, H(x)= 1 if x> 1". We can fit it to f by taking H(x- 4000).

f(x)= x/20000 + H(x- 4000)(4000- x/2000)

If x\le4000, H(x- 4000)= 0 so f(x)= 1/2000. If x> 4000, H(x- 4000)= 1 so f(x)= 1/2000+ 4000- x/2000= 4000.