Derivative is an important part of differential calculus, an important tool to study function properties and curve behavior, and an important method to solve some optimization problems in real life. This paper probes into the methods of using derivatives to solve the related problems such as materials, costs, profits and site selection in real life.
Derivative, also called wechat quotient, is a special limit, which reflects the speed at which the dependent variable changes with the independent variable in a function. It is an important basic concept in calculus and a bridge between elementary mathematics and advanced mathematics.
It plays an important role in learning geometry and proving inequalities. It also plays an important role in exploring the properties of functions, finding the extreme and maximum values of functions, and drawing graphs of functions. At the same time, it also provides an important method to solve some practical application problems.
In real life, we often encounter some problems related to economy or scientific research, such as seeking to maximize profits and minimize consumables, or maximizing efficiency and optimizing site selection. These problems are called optimization problems. How to find the best solution of these problems is the key to solve these problems, and these problems can be solved simply by derivatives, thus truly solving our real life problems.
Methods and precautions for solving optimization problems with derivatives: In real life, optimization problems, such as optimal location, minimum material consumption, maximum profit, etc., are essentially maximum problems, which are closely related to finding the maximum value of functions, and these problems can be transformed into function problems and solved simply by using derivative knowledge.
The method to solve the optimization problem: first, analyze the real problem, find out the relationship between variables, establish the corresponding functional relationship, and transform the real problem into a mathematical problem expressed by functions.
Then, the definition domain of the independent variable is determined according to the actual situation, creating the situation that the function seeks the maximum value in the closed interval. Finding the maximum (minimum) value of a function is obtained by deriving the function, determining the stagnation point and the non-derivative point, and comparing the function values of the endpoint, extreme point and non-derivative point of the interval. Finally, the mathematical problem is returned to the real problem, and the optimal scheme or strategy of the optimization problem is answered according to the answer of the mathematical problem.