Cubic function - Informative

09-06  Source: Network gathering  Views:1 

Advertisement

Cubic function - Informative

Functions of the third degree are turning parabolas.

What is a function of the third degree?

Third degree functions you will encounter mostly associated with polynomials, and very rational functions. For such a function is nothing more than a third degree polynomial. But what is that?

  • In third-degree polynomials, the highest occurring power for the variable is x³. The function equation is f (x) = bx + cx + ax³ + d. The coefficients a, b, c and d are real numbers. It should not be zero a, otherwise the degree of function would not "3", but only "2".
  • Examples of functions of the third degree are f (x) = 2x³ - 5x +7 or f (x) = 1/2 x³ - 4. The very simple power function f (x) = is x³ course such a third-degree polynomial in however, the b = c = d = 0 and a = 1.

The graph is a parabola turning

If one draws the graph to all rational functions of the third degree, the result is called turning parabolas. It is an upwardly open parabola, which merges into a downwardly parabola at the inflection point.

  • Depending on how close together move the two parabola components, formed wider or narrower graphs. In the extreme case the respective second Parabelast completely missing, as the graph of the function f (x) = X³ shows.
  • All functions of the third degree have an inflection point (B f ​​'' (x) = 0).; in the case of f (x) = X³ is it even to a saddle point (in addition f '(x) = 0).
  • Almost all functions of the third degree (except f (x) = ax³ + d) have extreme values, namely a maximum and a minimum, resulting from the two parabolic halves. To calculate these extremes with the first derivative f '(x) = 0 and has to solve a quadratic equation.
  • The zeros of such polynomials to calculate, however, can cause difficulties in some cases, as a third degree equation must be solved. Unfortunately for this purpose is not a formula (such as the pq-formula) available.
Related articles
  • Cubic function - Informative 09-06

    Functions of the third degree are turning parabolas. What is a function of the third degree? Third degree functions you will encounter mostly associated with polynomials, and very rational functions. For such a function is nothing more than a third d

  • Cubic function - a simple explanation 01-02

    A cubic function - what was that again? A cubic function - what is it? A cubic function is nothing other than a polynomial of the third degree, that is a function f: R-> R having the form f (x) = ax 3 + bx 2 + cx + d has, wherein the parameters a, b,

  • Cubic units - Informative 03-05

    Water consumption in cubic meters. knipseline / Pixelio The volume of a body or substance provides information on its physical size. It is also called volume. The cubic units are the units for it. The symbol for volume is a "V" This is volume in

  • Rhetorical means and their function - Information and examples on chiasmus and Ellipse 01-15

    Who knows rhetorical devices, need not worry. With the use of rhetorical devices a specific function is connected in many texts, which makes it easier for the reader to interpret the relevant statements correctly. In the following article you will fi

  • Transfer functions - Informative 05-20

    Who can solve transfer tasks, it has made it easier at school and in life. The key to successful learning: Transfer tasks Transfer tasks at school or university to test whether you have the ability to transfer a learned facts or problem solving in a

  • Cubic growth - Declaration 05-30

    Growth processes can be modeled with the aid of growth functions. Cubic growth - some basic considerations In school you have probably never heard the term cubic growth. Cubic functions you have most likely very well acquainted. These have the form f

  • Ganzrationale functions - which should be considered when calculating 04-11

    It is yet allowed to ask again! Ganzrationale functions - so go ahead when calculating A very rational function is always a sum of exponential functions (of varying degrees), with coefficients (numbers before the powers) are provided. An example of a

  • take deep well pump properly in operation 08-27

    A Tiefbrunnenpumpe promotes your water upstream. There are very different Deep Well Pump Basically, deep well pumps are always required when the height difference between the pumped water and the pump inlet is more than nine meters. Deep well pumps a

  • H-Rotor - DIY 03-25

    Specifications, sketch, example of a proven concept from Taiwan and Wind Map Germany The H-rotor is a Vertikalachswindturbine The H is the outer shape of the rotor. It is a design that uses the drag, wind pressure to the back ground. This is not a go

  • Function of ATP in metabolism - Informative 07-09

    The energy that we absorb from food is converted into ATP in the body. Energy metabolism and ATP For the contraction of a muscle energy is necessary; this comes from chemical reactions that occur in the body. When muscles work so chemical energy is c

  • The mercury vapor lamp - useful information about the function 03-09

    Street lighting often contain mercury vapor lamps. Christoph_S. / Pixelio The mercury vapor lamp and their types In the mercury lamp, which is also referred to as mercury vapor discharge lamp is a so-called gas-discharge lamp. In these light sources

  • An orthopedic pillow under test - Find out more about the function and effect 01-07

    Find a sound sleep with the right pillow. PeeF / Pixelio An orthopedic pad is not equal to the other. Different functions you can achieve different effects with the pillow. Often it can be to find out if you feel comfortable with the new pillow at al

  • simply stated power series expansion of a function 02-13

    Frequently, difficult mathematical formulas with a simple derivation understand. Development of a function in a series Mac Laurinsche Of course it can not be any function in a power series develop. Rather, a function must meet certain criteria, so th

  • Navi: CarTrek 700 - useful information about the device 02-23

    The CarTrek 700 takes you reliably. The favorable Navi CarTrek 700 The navigation system is offered for an on the internet and on the other in the various net-market and costs depending on the provider just under 60 euros. With this deal you can get

  • Simyo: SIM card number - Informative 03-16

    The SIM card number of Simyo is on the map. Background of the SIM card number The SIM card number is for the purpose that it is so identifiable. For this reason, the numbers are only paid once. Simyo stores important information on the small chip car

  • Meeting path-time function: different starting points - calculation 03-25

    Drive trains toward each other, they meet at some point. Create functions for different starting points, distance and time If you want to solve a problem of the type described, it is essential that you have information about the distance to be travel

  • The Follow-me-home function 05-16

    With the follow-me-home function will show afterglow spotlight the way to the front door. Comfortable lighting comfort with standard Follow-Me-Home What vehicles like the Opel Meriva, Toyota Corola, Peugeot 308, Lancia Ypsilon, Toyota Auris, Fiat Bra

  • How long does a Schufa information? - Find out the procedure 08-04

    Forms for Schufa information is available online. Since 1 April 2010 you have the right to receive once a year for free information about detected and evaluated data of the last twelve months by agencies such as the Schufa. Money that does not cost o

  • What is a wireless stick? - Function simply explained 09-04

    The WLAN stick helps mobile surfing. Gerd_Altmann_Shapes_photoshopgraphics.com / Pixelio The WLAN stick you to the Internet At the beginning of the Internet, all equipment had to be connected by LAN. The acronym stands for Local Area Network and work

  • reshape function term in peak form - how it works 09-19

    Forming in the vertex form is not so difficult. General on the vertex form The peak form is the form of a quadratic equation, from which can be seen a vertex immediately. Moreover, this form of the equation tells you whether the associated parabola i