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

Volume and surface area, a conical hole drilled in a circular cylinder of h...

a conical hole drilled in a circular cylinder of height 12 and radius 5cm the height and radius of cone are also same find volume

Numerical analysis and computer techniques, write a fortan programme to gen...

write a fortan programme to generate prime number between 1 to 100

Calculate the net amount and distance, 1. A train on the Bay Area Rapid Tra...

1. A train on the Bay Area Rapid Transit system has the ability to accelerate to 80 miles/hour in half a minute. A.   Express the acceleration in miles per hour per minute. B

Calculus , Mean, variance, skewness and kurtosis of a probability density f...

Mean, variance, skewness and kurtosis of a probability density function f(r)that has a distribution of a passive scalar filed in a stationary isotropic turbulence for initial condi

Case let, How should Shoppers’ Stop develop its demand forecasts?

How should Shoppers’ Stop develop its demand forecasts?

Problem solving, if you start a business and john creates 6 t shirts more t...

if you start a business and john creates 6 t shirts more than pedro and pedro four t shirts less than eva and between the three of then made 22 tshirts, how many t-shirts made each

Callie grandmother pledged $0.50 for each mile callie walked, Callie's gran...

Callie's grandmother pledged $0.50 for each mile Callie walked in her walk-a-thon. Callie walked 9 miles. How much does her grandmother owe? Multiply the number of miles (9) th

MATH HELP: URGENT, the andersons are buying a new home and need to fence th...

the andersons are buying a new home and need to fence their yard. the yard is 40 ft by 80 ft. each fencing section is 8ft. how many sections will they need?how many posts will they

integral 0 to pi e^cosx cos (sinx) dx, Let u = sin(x). Then du = cos(x) dx...

Let u = sin(x). Then du = cos(x) dx. So you can now antidifferentiate e^u du. This is e^u + C = e^sin(x) + C.  Then substitute your range 0 to pi. e^sin (pi)-e^sin(0) =0-0 =0

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