How can MATLAB help in finding an equation for a given curve?

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To find a single equation for a given curve using MATLAB, a piecewise linear function can be utilized, such as f(x) = x/2000 for x ≤ 4000 and f(x) = 2 for x > 4000. For a more unified expression, the Heaviside function H(x) can be applied, allowing for the formulation f(x) = x/20000 + H(x - 4000)(4000 - x/2000). This approach effectively differentiates the behavior of the function based on the value of x. The discussion highlights the versatility of MATLAB in modeling curves through mathematical expressions.
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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
 

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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.
 

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