Newton’s Method and Numerical Derivatives to Find the Minimum of f(x) Solve Example 3.2 as a single-variable minimization problem using Newton’s method. For the first trial point, use the ideal gas...

Newton’s Method and Numerical Derivatives to Find the Minimum of f(x) Solve Example 3.2 as a single-variable minimization problem using Newton’s method. For the first trial point, use the ideal gas result, υ[ ] . . 1 3 = = 6 39 RT P ft /lb-mol The reader can find background material for this application of Newton’s method in Ravindran et al. (2006). Recall from Problem 3.4 that in Newton’s method, we found the roots of the polynomial f(x) = 0 by using a linear approximation to f(x) at x[1]. In this application of Newton’s method, we are again “looking for the roots of a polynomial,” but here, the polynomial is f′(x) = 0. Recall from calculus that a necessary condition for the minimum of a function is f′(x) = 0. A linear approximation of f′(x) at x[1] can be constructed as