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

Basic differential equation, Two 1000 liter tanks are containing salt water...

Two 1000 liter tanks are containing salt water. Tank 1 has 800 liters of water initially having 20 grams of salt dissolved in this and tank 2 has 1000 liters of water and initially

Most crucial aspect of learning multiplication, Which of the following is t...

Which of the following is the most crucial aspect of learning multiplication? i) Multiplication facts ii) Recall of tables and their recitation iii) Understanding "how man

#title applications of vector and scalar , #question application of vector ...

#question application of vector and scalar in our daily life

Applications of markov chains in business, please help me in my assignment,...

please help me in my assignment, explain Applications of Markov Chains in Business.

Add subtract fractions., how do you add and subtract mixed numbers with fra...

how do you add and subtract mixed numbers with fractions

Operation research, interestind topic in operation research for doing proje...

interestind topic in operation research for doing project for msc mathematics

Geometry, what shapes can go into a triangular prism

what shapes can go into a triangular prism

Trignometry, prove that cos(a)/1-sin(a)=tan(45+A/2)

prove that cos(a)/1-sin(a)=tan(45+A/2)

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