Like y=ax? +bx？ The function of +CX+d (a ≠ 0, B, C and D are constants) is called cubic function. The image of cubic function is a curve-regression parabola (different from ordinary parabola).

Five key points of cubic function behavior;

1, the number of extreme points of cubic function y=f(x) on (-∞,+∞).

2. The number of times the image of cubic function y=f(x) intersects with the X axis.

3. Monotonicity.

4. The number of tangents of cubic function f(x) image.

5. Combining cubic function and inequality, create a situation and find the range of parameters.

Function:

Mathematical definition of function: Given a set of non-empty numbers A, the corresponding rule F is applied to A, denoted as f(A), and another set of numbers B is obtained, namely B=f(A). Then this relationship is called functional relationship, or function for short.

Simply put, for two variables X and Y, if each given value of X has a unique definite value corresponding to it, then we say that Y is a function of X ... where X is called an independent variable and Y is called a dependent variable.

Let the domain of the function f(x) be D, and the number set X is contained in D. If the number K 1 exists, so that f(x)≤K 1 holds for any x∈X, the function f(x) is said to have an upper bound on x, and K 1 is called the function f. If there is a number K2, so that f(x)≥K2 holds for any x∈X, the function f(x) is said to have a lower bound on x, and K2 is called a lower bound on the function f(x).

If there is a positive number m, so that |f(x)|≤M holds for any x∈X, the function f(x) is said to be bounded on X. If there is no such m, the function f(x) is said to be unbounded on X. The necessary and sufficient condition for the function f(x) to be bounded on X is that it has upper and lower bounds at the same time.