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

Rules for inequalities, Here we look at only the rules without going ...

Here we look at only the rules without going into their proofs. They are: a  0. If a If a If a

Communicating the meaning of addition, COMMUNICATING THE MEANING OF ADDITIO...

COMMUNICATING THE MEANING OF ADDITION :  One of the characters in a novel written by the Malayalam writer Vaikom Muhammed Basheer was asked by his teacher, "How much is one and on

How many more cm are required to reach the average monthly, Thomas is remai...

Thomas is remaining track of the rainfall in the month of May for his science project. The first day, 2.6 cm of rain fell. On the second day, 3.4 cm fell. On the third day, 2.1 cm

Laura paid $17 for jeans what was original price of jeans, Laura paid $17 f...

Laura paid $17 for a pair of jeans. The ticketed price was 20% off the original price plus the sign on the rack said, "Take an additional 15% off the ticketed price." What was the

Shares and dividends, I need to make an assignment on this topic what shoul...

I need to make an assignment on this topic what should i write in it

Measures of dispersion- measures of central tendency, Measures of Dispersio...

Measures of Dispersion - The measures of dispersion are extremely useful in statistical work since they indicate whether the rest of the data are scattered away from the mean

Permutation, HOW MANY number laying between 100 and 1000 can be formed with...

HOW MANY number laying between 100 and 1000 can be formed with 0,1,2,3,4,5 and also divisible by 5 with distinct digit

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