First, the application of derivatives.
1. Study the maximum value of a function with derivatives.
Make sure that the function is differentiable in its definition domain (usually open interval), find out the zero point of the derivative function in the definition domain, and study the monotonicity of the function around zero point. If the left side increases and the right side decreases, the function will reach the maximum at this zero point. If the left side shrinks.
Increase on the right, then the function of zero takes the minimum value. After learning how to study the maximum value of a function with derivatives, you can do a comprehensive problem about derivatives and functions to test your learning effect.
2. Common function optimization problems in life.
1) cost and minimum cost.
2) the problem of profit and income
3) The biggest problem of area and volume.
Second, reasoning and proof.
Inductive reasoning: Inductive reasoning is a key content of senior two mathematics, and its difficulty lies in that some conclusions lead to general conclusions. The solution is to fully consider the information provided by some conclusions and find general rules from them. The difficulty of analogical reasoning is to find the similar characteristics of two kinds of objects and get the characteristics of the other from the characteristics of one kind of objects.
The method of cracking is to analyze the relationship between two kinds of objects by using the already mastered mathematical knowledge, and obtain the required similar features through the known similar features of two kinds of objects.
2. Analogical reasoning: It is called analogical reasoning to infer that two objects have some similar characteristics and some known characteristics of one object. In short, analogical reasoning is from special to special.
Third, inequality.
Discussion on the solution of one-variable quadratic inequality with parameters
1) Quadratic coefficient: If the quadratic coefficient contains letters, it should be discussed in three situations: the quadratic coefficient is positive, zero and negative.
2) The root of the equation corresponding to the inequality: If the root of the equation corresponding to the unary quadratic inequality can be found by factorization, then discuss the classification according to the size of the two roots. At this time, the size relationship between the two roots is the classification standard. If the root of the equation corresponding to the unary quadratic inequality cannot be found by factorization,
Then, it is classified and discussed according to the discriminant of the equation. Inequality exercises can help you use the knowledge of inequality more skillfully, such as the skills of proving inequality with scale and the nine skills of finding the maximum value with mean inequality, which need to be summarized in the process of doing the problem.