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

Progressions, The sum of the series 1+1/2+1/4+......is

The sum of the series 1+1/2+1/4+......is

Unitary Method Sample Questions, Where can I find sample questions of Unita...

Where can I find sample questions of Unitary Method for kids to practice? I need  Unitary Method  study material if availbale here on website, i found there is very useful material

Absolute convergent, Find out if each of the subsequent series are absolute...

Find out if each of the subsequent series are absolute convergent, conditionally convergent or divergent. Solution: (a) The above is the alternating harmonic ser

Using calculus method, Sheldon as the day for the challenge gets closer wan...

Sheldon as the day for the challenge gets closer wants to enter the race. Not being content with an equal start, he wants to handicap himself by giving the other yachts a head star

On income and return from shares, a company declares a semu annual dividend...

a company declares a semu annual dividend on 5%.a man has 400 shares of the company.if his annual income from the share is rs 1000 find the face value of each share?

Help, sin(x)+cos(x)

sin(x)+cos(x)

Where is the bus in relation to the hotel, A bus picks up a group of touris...

A bus picks up a group of tourists at a hotel. The sightseeing bus travels 2 blocks north, 2 blocks east, 1 block south, 2 blocks east, and 1 block south. Where is the bus in relat

Shares and dividend, a man in rested rupee 800 is buying rupee 5 shares and...

a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit

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