Cubic function - Informative

09-06  Source: Network gathering  Views:1 


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.
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