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

Local maxima, Given that f(x,y) = 3xy -  x 2 y  - xy 2 . Fi nd all the poin...

Given that f(x,y) = 3xy -  x 2 y  - xy 2 . Fi nd all the points on the surface z = f(x, y)where local maxima, local minima, or saddles occur

Minima, Minima, Maxima and points of inflexion a)      Test for rela...

Minima, Maxima and points of inflexion a)      Test for relative maximum Consider the given function of x whose graph is presented by the figure given below

Solid Mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

gauss elimination method , Question: Use  Gauss elimination method to ...

Question: Use  Gauss elimination method to solve the following system of equations.  -y +3z=4  2x-y-2z= 2  2x-2y+z =6  4x-y-7z= 0

Stuck on this, I need help on radical notation for a homework assignment I'...

I need help on radical notation for a homework assignment I''m really confused on it. Can I get help?

What are various strategies adopted for learning maths, Give some children ...

Give some children around you a task in mathematics. The task should be in an area in which they' have not been given a large dose of algorithms and strategies. Do all of them foll

Determine the actual viewing area, Computer monitors are calculated by thei...

Computer monitors are calculated by their diagonals. If a monitor is advertised to be 19 in, Determine the actual viewing area, considerthe screen is square? (Round to the nearest

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