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

Proof of alternating series test, Proof of Alternating Series Test With...

Proof of Alternating Series Test With no loss of generality we can assume that the series begins at n =1. If not we could change the proof below to meet the new starting place

Example of division , Example of division: Divide 738 by 83. Soluti...

Example of division: Divide 738 by 83. Solution: Example: Divide 6409 by 28. Solution: Division could be verified through multiplying

Plot your data on a scatter plot, Devise data that link a certain relations...

Devise data that link a certain relationship OF YOUR CHOOSING between two variables. Write a rationale stating why you chose this particular data and what you are planning to STAT

Calculate time interval, From top of a tower a stone is thrown up and it re...

From top of a tower a stone is thrown up and it reaches the ground in time t1. A second stone is thrown down with the same speed and it reaches the ground in t2. A third stone is r

What is stem-and-leaf plots, Q. What is Stem-and-Leaf Plots? Ans. ...

Q. What is Stem-and-Leaf Plots? Ans. A stem-and-leaf plot is a table that provides a quick way to arrange a set of data and view its shape, or distribution. Each data val

Example of exponential smoothing, Example of Exponential Smoothing ...

Example of Exponential Smoothing By using the previous example and smoothing constant 0.3 generate monthly forecasts Months Sales Forecast

Lpp, A paper mill produces two grades of paper viz., X and Y. Because of ra...

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Operation on polynomial, Perform the denoted operation for each of the foll...

Perform the denoted operation for each of the following.  (a) Add 6x 5 -10x 2 + x - 45 to 13x 2 - 9 x + 4 .   (b) Subtract 5x 3 - 9 x 2 + x - 3 from       x 2+ x +1.

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