Polynomial Plot Mini-project


Interactive Newton's Method




This is a simple tool that demonstrates the overall concept of optimization. The fundamental idea is:

If a process can be defined parametrically, as a collection of inputs X, that lead to an output, f(X); then, a minimum (or maximum) of the output can be found by examining the gradients (changes of the inputs wrt the outputs) of the process at any set of inputs that is sufficiently close to the desired min/max.

By applying Newton's Method, an iteration of better guesses can be generated, each in the beneficial direction toward that min/max.

For example, consider the simple, one-dimensional polynomial of the form:

A*(x+D)^3 + B*(x+D)^2 + C*(x+D) + Z


Instructions:
  1. Fill in the coefficients that define the polynomial
  2. Make a guess of the minimum (see the table below)
  3. Define the feasible range of guesses (i.e. the Lower and Upper Bounds)
Once all the input information is set, then press the "Find the Next Step" button below. The guess of X will project to the next best guess of X each time you press the button... until there is essentially no more room for improvement.



Polynomial Coeffcients and Horizontal/Vertical Shifts

Cubic A:
Quadratic B:
Linear C:
Vert Shift (Z):
Horiz Shift (D):







**** PLOT ****


Lower Bound Upper Bound



Newton Method Info

Initial value of x:
F(x):
2nd Der @ x:
1st Der @ x:
Change of x:
Projected value of x:







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