1, derivative method
Firstly, take the derivative of the function, make the derivative function equal to zero, get the value of X, and judge the relationship between X and the derivative function. When the derivative function is greater than zero, it is a increasing function, and when it is less than zero, it is a subtraction function.
2. Definition method
Let x 1, x2 is any two numbers in the domain of function f(x), and x1< x2; If F (X 1) < F (x2), then this function is an increasing function; Conversely, if f (x 1) > f (x2), then this function is a subtraction function.
3. Natural methods
If the functions f(x) and g(x) are monotonic in the interval b, there are:
(1) f (x) and f (x)+c (c is a constant) have the same monotonicity;
(2) f (x) and c? F(x) has the same monotonicity when c > 0 and the opposite monotonicity when c < 0;
(3) When f(x) and g(x) are both increasing (decreasing) functions, then F (x)+G (x) are both increasing (decreasing) functions;
(4) When f(x) and g(x) are both increasing (decreasing) functions, then f(x)? G(x) is also an increase (decrease) function when both are constants greater than 0, and is also an increase (decrease) function when both are constants less than 0;
4. Compound function with addition and subtraction.
For the compound function y = f [g (x)] (pay attention to the range of the inner function) and t = g (x) that satisfies the method of "increasing with different decreasing", then if two of the three functions y = f (t), t = g (x) and y = f [g (x)] have the same monotonicity, if
Origin of function
The word "function" used in China's math book is translated. It was Li, an algebra expert in China's Qing Dynasty, who translated "function" into "function" when he translated Algebra (1859).
In ancient China, the word "Xin" and the word "Han" were universal and both had the meaning of "Han". Li's definition is: "every formula contains heaven, which is a function of heaven." In ancient China, four different unknowns or variables were represented by four words: heaven, earth, people and things.
The meaning of this definition: "Whenever a formula contains a variable X, the formula is called a function of X", so "function" means that the formula contains variables. The exact definition of an equation refers to an equation containing unknowns. However, in the early mathematical monograph "Nine Chapters Arithmetic" in China, the word "equation" means simultaneous linear equations with many unknowns, which are called linear equations.