The difference and connection between extreme value and maximum value: the difference lies in their different concepts. Compared with its two sides, the extreme value is the maximum when it is greater than the two sides, and the minimum when it is less than the two sides; The maximum value is the maximum and minimum value of the function within the defined domain or specified interval. Except for a specific function, the two are not necessarily related.
Connection: in some cases, the function has an extreme value and no maximum value; In other cases, the function has a maximum and no value, in other cases, maximum = extreme value.
Extreme value is the maximum or minimum value of a function. If a function has a value everywhere in the neighborhood of a point, and the value of that point is the maximum (minimum), then the value of this function at that point is the maximum (minimum). If it is greater than (less than) the function values of other points in the neighborhood, it is a strict maximum (less than). This point is correspondingly called extreme point or strict extreme point.
Knowledge expansion
To learn high school mathematics well, there are several key learning methods and skills that can help you:
Determine your own learning goals: Before you start learning, make clear your learning goals, such as what kind of results you hope to achieve in the exam, or understand some specific mathematical concepts. Setting clear goals helps to guide learning and provide motivation.
Understand basic concepts: high school mathematics is based on basic concepts. Make sure you have a clear understanding of basic mathematical concepts, such as algebra, geometry, functions, etc. If you find some aspects difficult, you can review your junior high school math knowledge or ask your teacher for help.
Deliberate practice: Mathematics is a subject that needs repeated practice. Practice can not only consolidate what you have learned, but also help you improve your problem-solving ability. Arrange a certain time to practice deliberately every day, complete the exercises and do more related application problems.
Diversified learning resources: In addition to the textbooks and learning materials provided by teachers, you can also find other learning resources to help you learn high school mathematics. For example, you can find related online video tutorials, reference books, exercises and so on. Diversified learning resources help you understand and apply mathematical concepts in different ways.
Reasonable arrangement of study time: Reasonable arrangement of study time is very important. Make a fixed study schedule to ensure that you have a certain amount of time to concentrate on studying high school mathematics every day. Avoid procrastination, stay focused and improve learning efficiency.
Participate in discussion and problem solving: It is a good learning method to discuss and solve problems with classmates. Participating in math study groups, solving problems, sharing ideas with classmates and discussing problem-solving methods can help you understand math knowledge deeply.
Ask for help: If you encounter difficulties in your study, don't hesitate to ask for help. Asking questions to teachers, discussing with classmates and looking for a tutor are all ways to get help. Make sure you understand the difficulties before you can learn smoothly.
Generally speaking, learning high school mathematics requires persistence and care. Through continuous practice, understanding the basic concepts, arranging time reasonably and actively seeking help, I believe you can achieve good results.