What is Monotonicity?

The monotonicity of a function can also be called the increase or decrease of a function. When the independent variable of the function f ( x ) increases (or decreases) within its defined interval, the value of the function f ( x ) also increases (or decreases), then the function is said to have Monotonic.

The monotonicity of a function is also called the increase or decrease of the function.

Generally, let s set one

Image properties

1.Image observation method

As described above, in the monotonic interval, the image of the increasing function is rising, and the image of the decreasing function is falling. Therefore, in a certain interval, the function that keeps rising

Using function monotony can solve many function-related problems. Through the study of the monotonicity of functions, it is helpful to deepen the grasp and deepening of the knowledge of functions, and to convert some practical problems into using the monotonicity of functions to deal with. Therefore, the discussion of the monotonicity of the function is only of important theoretical value, and has good application value. This article combines the analysis of some typical examples to illustrate the application of monotonicity of functions, such as using the monotonicity of functions to find the maximum value, solve equations, and prove small equations. ^[6]

1.Using function monotonicity to find the maximum value

There are many ways to find the maximum (small) value of a function, but the basic method is to determine by the monotonicity of the function, especially for small derivable continuous points, the maximum (small) value in the open area or the infinite area. Analysis is generally judged by monotonicity.

2 Solving equations using functions monotonicity

Function monotonicity is a very important property of functions.

In x and y, there is a one-to-one correspondence, so that we can transform complex equations into types such as "

"To solve the problem by using the monotonicity of the function x = a to simplify the problem, and constructing a monotonic function is the key to solving the problem.

3. Prove Inequalities Using Function Monotonicity

First, a monotone function is constructed according to the characteristics of the small equation. Second, it is determined that the function is a monotonic function in a certain area [a, b]. Finally, the small equation we want to prove is obtained from the definition of the monotone function.