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

Fractions, if you have 1/5 of a candy bar and 4 friends how much will they ...

if you have 1/5 of a candy bar and 4 friends how much will they get

Discrete uniform distribution, Discrete Uniform Distribution Acme Limit...

Discrete Uniform Distribution Acme Limited is a car manufacturer. The company can paint the car in 3 possible colors: White, Black and Blue. Until the population is sampled, th

Find extrema & relative extrema f ( x ) = x3 on [-2, Recognizes the absolut...

Recognizes the absolute extrema & relative extrema for the given function.                                                    f ( x ) = x 3      on        [-2, 2] Solution :

Inflation , Inflation The inflation rate for a given period can be ca...

Inflation The inflation rate for a given period can be calculated using the following formula; Inflation = (current retail price index/retail price index in the base year)

Why is vector division undefined, Division basically refers to multiplicati...

Division basically refers to multiplication of reciprocal. For example a/b is same as a*1/b or we can say, is same as a*b -1 , which is "a" multiplied to the inverse of "b". There

In the terms of x, The length of Kara's rectangular patio can be expressed ...

The length of Kara's rectangular patio can be expressed as 2x - 1 and the width can be expressed as x + 6. In the terms of x, what is the area of her patio? Since the area of a

Experiments probabillity of compound events, what is the expiremental proba...

what is the expiremental probability that the next toss and spin will result in 3 and tail if 1-heads,53.2-heads,49.3-heads,54.1-tail,65.2-tails,71.3-tails,62

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