Optimization, Mathematics

Assignment Help:

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                                          


Related Discussions:- Optimization

How to solve systems of equations, How to solve Systems of Equations ? ...

How to solve Systems of Equations ? There's a simple method that you can use to solve most of the systems of equations you'll encounter in Calculus. It's called the "substitut

Define tautology and contradiction, Define tautology and contradiction.  ...

Define tautology and contradiction.  Ans: If a compound proposition comprises two atomic propositions as components, after that the truth table for the compound proposition con

Determine the average bit rate - huffman codebook, 1. Consider a source wi...

1. Consider a source with 4 symbols {a,b,c,d}. The probability of the 4 symbols are P(a)=0.4, p(b) = 0.1, p(c)=0.2, p(d)= 0.3. a. Design a Huffman codebook for these symbols.

Differentiate product rule functions, Differentiate following functions. ...

Differentiate following functions. Solution At this point there in fact isn't a lot of cause to use the product rule.  We will utilize the product rule.  As we add

Each child is unique in learning development, Each Child Is Unique :  Alth...

Each Child Is Unique :  Although every child goes through similar stages of development, the process may vary from one set of children to another, and also from one child to anoth

prove that x = 2h/3, A vertical post stands on a horizontal plane.  The an...

A vertical post stands on a horizontal plane.  The angle of elevation of the top is 60 o and that of a point x metre be the height of the post, then prove that x = 2 h/3 .

Word problems, Ana has hiked 4 1/2 miles. She is 2/3 of the way along the t...

Ana has hiked 4 1/2 miles. She is 2/3 of the way along the trail. How long is the trail?

Simplification, 4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd