1, discriminant for maximum.
It is mainly suitable for functions that can be transformed into quadratic equations about independent variables. According to the characteristics of quadratic equation image, the opening direction and extreme point can be found.
2. Monotonicity of functions
Firstly, the monotonicity of the function in a given interval is determined, and then the maximum value of the function is found according to the monotonicity.
3. Combination of numbers and shapes
It is mainly suitable for functions with clear geometric figures, and the maximum value of the function can be found through geometric models.
Extended data:
The method of finding the extreme value of function
The method of finding the maximum value of the function is as follows:?
1. matching method: a function with a shape, 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: the fractional function in the form of is transformed into a quadratic equation about X with coefficient y, and it is easy to generate roots when finding the maximum value of Y, 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. When using mean inequality, shape function sum ≥≤, pay attention to the application conditions of positive and definite. , that is, a and b are both positive numbers, both are fixed values, and 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 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?
6. The combination of numbers and shapes is like taking the left side of the formula as a function and the right side as a function, putting their images in the same coordinate system, observing their positional relationship, and using analytic geometry knowledge to find the maximum value.
References:
Baidu encyclopedia-minimum value