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4. Process Modeling
4.8. Some Useful Functions for Process Modeling
4.8.1. Univariate Functions
4.8.1.1. Polynomial Functions

4.8.1.1.3.

Cubic Polynomial

example of cubic polynomials
Function: \( \displaystyle f(x) = \beta_0 + \beta_1x + \beta_2x^2 + \beta_3x^3, \ \ \beta_3 \neq 0 \)
Function
Family:

Polynomial
Statistical
Type:

Linear
Domain: \( \displaystyle (-\infty, \ \infty) \)
Range: \( \displaystyle (-\infty, \ \infty) \)
Special
Features:

None
Additional
Examples:
cubic polynomial example 1: y = -6*(x+2)*x*(x-2); -2 < x < 2
cubic polynomial example 2: y = (x-25)**3 + 450; 20 < x < 30
cubic polynomial example 3: y = -6*(x+2)*x*(x-1); -1 < x < 0.5
cubic polynomial example 4: y = (x-25)**3 + 450; 30 < x < 40
cubic polynomial example 5: y = (x-25)**3 + 450; 15 < x < 20
cubic polynomial example 6: y = -6*(x+2)*x*(x-1); -3 < x < -1.5
cubic polynomial example 7: y = -6*(x+2)*x*(x-1); 1 < x < 2
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