Optimization, Mathematics

Optimization is required in situations that frequently arise in finance and other areas. Organizations would like to maximize their profits or minimize their costs at a given level of output. An individual would like to maximize his utility when choosing investment alternatives. If we have a mathematical function, then we can find a solution to the optimization problem using calculus.

Of all the higher order derivatives, the second order derivative is of special interest in problems of optimization.

The first derivative of a function, f'x is the slope of the function f(x), or the rate of change in the value of f(x) per unit change in x. Similarly the second derivative, f''x is the slope of the function f'x or the rate of change in the value of f'x per unit change in x, which is the rate of change of the original function f(x).

The following figures and table show various combinations of signs of f'x and f''x and the implied slope of the graph of f(x).

781_optimization.png

  f'x

  f''x

f(x) is


positive

positive

increasing at an increasing rate

positive

negative

increasing at a decreasing rate

negative

positive

decreasing at an increasing rate

negative

negative

decreasing at a decreasing rate                                          

Posted Date: 9/13/2012 7:14:08 AM | Location : United States







Related Discussions:- Optimization, Assignment Help, Ask Question on Optimization, Get Answer, Expert's Help, Optimization Discussions

Write discussion on Optimization
Your posts are moderated
Related Questions
in the form of linear graph interpret the ralationship between two quantities

Definite integration It involve integration among specified limits, say a and b The integral    is a definite integral whether the limits of integration are as: a and b

how is the male orgasm?

The vertices of a ? ABC are A(4, 6), B(1. 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that AD/AB = AE/AC = 1/4 .Calculate the  ar

Three shirts and five ties cost $23. Five shirts and one tie cost $20. What is the price of one shirt? Let x = the cost of one shirt. Let y = the cost of one tie. The ?rst part

Q. Show Inverse Trigonometric Functions? Ans. Many functions, including trig functions, are invertible. The inverse of trig functions are called ‘inverse trig functions'.

Use Newton's Method to find out an approximation to the solution to cos x = x which lies in the interval [0,2].  Determine the approximation to six decimal places. Solution

E1) I have a three-year-old friend. He has a lot of toy cars to play with. Playing with him once, I divided the cars into two sets. One set was more spread out and had 14 cars in i

Find out the determinant: Find out the determinant of the following 3 x 3 matrix, expanding about row 1. Solution:

THE PREREQUISITES FOR MULTIPLICATION : The word 'multiply', used in ordinary language, bears the meaning 'increase enormously For instance, bacteria multiply in favourable conditi