Analysis Homework #4 Solutions 1. 2.
... 4. Find the min and max values of f (x) = 3x4 − 16x3 + 18x2 over [−1, 1]. • Since f is continuous on a closed interval, it suffices to check the endpoints, the points at which f ′ does not exist and the points at which f ′ is equal to zero. In this case, f ′ (x) = 12x3 − 48x2 + 36x = 12x(x2 − 4x + 3) ...
... 4. Find the min and max values of f (x) = 3x4 − 16x3 + 18x2 over [−1, 1]. • Since f is continuous on a closed interval, it suffices to check the endpoints, the points at which f ′ does not exist and the points at which f ′ is equal to zero. In this case, f ′ (x) = 12x3 − 48x2 + 36x = 12x(x2 − 4x + 3) ...
Introduction
... (defun multiplier (n seq) (values (function (lambda () (* n (pop seq)))) (function (lambda () (not (null seq)))))) ...
... (defun multiplier (n seq) (values (function (lambda () (* n (pop seq)))) (function (lambda () (not (null seq)))))) ...
Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding ""best available"" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.