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

Difererntial equation, Ask queFind the normalized differential equation whi...

Ask queFind the normalized differential equation which has {x, xex} as its fundamental setstion #Minimum 100 words accepted#

Wants to Join as expert, Hi.. This is dinesh kumar I just joined experminds...

Hi.. This is dinesh kumar I just joined experminds.com , i wamt to receive assignment in maths and want to complete students assignment within time. Please help me how i can become

Trigonometry, how to change sin 24 degree in digits?

how to change sin 24 degree in digits?

Help, draw a right angle isosceles triangle with 9 triangles in it

draw a right angle isosceles triangle with 9 triangles in it

Functions, find the derived functions

find the derived functions

Pre-Calculus, Which point is the reflection through the origin (0, 0) of th...

Which point is the reflection through the origin (0, 0) of the point (-8, -9)?estion..

Profit and loss, a shopkeeper buys two cameras at the same price . he sells...

a shopkeeper buys two cameras at the same price . he sells one camera at a profit of 18% and the other at a price of 10% less than the selling price of the first camera. find his p

Equivelent ratios, if 2 ballons cost 12 coins,use equivelent ratios to see ...

if 2 ballons cost 12 coins,use equivelent ratios to see how many coins 8 ballons would cost

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

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