1. matching method: the function with the shape is, and the maximum value of the function is determined according to the value of the extreme point or boundary point of the quadratic function.

2. Discriminant method: a fractional function in the form of, which is transformed into a quadratic equation about X with coefficient y. Because finding the maximum value of Y is greater than or equal to 0, this method is prone to root growth, so it is necessary to check whether the corresponding value of X has a solution when finding the maximum value.

3. Using the monotonicity of the function: first define the domain and monotonicity of the function, and then find the maximum value.

4. Use the mean inequality, shape function, and the application conditions of greater than or equal to and less than or equal to pay attention to positive and definite. , that is, whether the equal sign of a=b is established.

5. Substitution method: a function in the form of, so that x can be reversed, and then the function about t can be obtained by substituting into the above formula. Pay attention to the range of the domain of t, and then find the maximum value of the function about t ... and the triangle method of substitution and the parameter method of substitution.

6. Combination of number and shape with normal shape: If the left side of the formula is regarded as a function and the right side as a function, put their images in the same coordinate system, observe their positional relationship, and use analytic geometry knowledge to find the maximum value. Find the maximum value of a shape with the slope formula of a straight line.

7. To find the maximum value of a function by derivative: firstly, the domain is required to be symmetrical about the origin, and then the relationship between f(x) and f(-x) is judged: if f(x)=f(-x), it is an even function; If f(x)=-f(-x), odd function.