The first part is the application of functions.
We have learned eight kinds of functions: linear function, quadratic function, fractional function, irrational function, power, exponent, logarithmic function and piecewise function. These functions reflect the dependence of variables in nature from different angles, so the knowledge of functions in algebra is closely related to production practice and life practice. Here we focus on the application of the first two types of functions.
Application of unary linear function
One-dimensional linear function is widely used in our daily life. When people are engaged in business, especially in consumer activities in social life, if the linear correlation of variables is involved, one-dimensional linear function can be used to solve the problem.
For example, when we shop, rent a car or stay in a hotel, operators often provide us with two or more payment schemes or preferential measures for publicity, promotion or other purposes. At this time, we should think twice, dig deep into the mathematical knowledge in our minds and make wise choices. As the saying goes: "From Nanjing to Beijing, it is better to buy than to sell." Never follow blindly, lest you fall into the small trap set by the merchants and suffer immediate losses.
The application of univariate quadratic function
When enterprises engage in large-scale production such as construction, breeding, afforestation and product manufacturing,
The relationship between profit and investment can generally be expressed by quadratic function. Business managers often predict the prospects of enterprise development and project development based on this knowledge. They can predict the future benefits of enterprises through the quadratic function relationship between investment and profit, so as to judge whether the economic benefits of enterprises have been improved, whether enterprises are in danger of being merged, and whether the project has development prospects. Common methods include: finding the maximum value of a function, the maximum value in a monotonous interval and the corresponding function value of an independent variable.
Third, the application of trigonometric functions
Trigonometric functions are widely used. Here only the simplest and most common type-the application of acute trigonometric function: the problem of "forest greening".
In forest greening, trees must be planted at equal distance on the hillside, and the distance between two trees on the hillside should be consistent with the distance between trees on the flat ground when projected on the flat ground. (as shown on the left) Therefore, foresters should calculate the distance between two trees on the hillside before planting trees. This requires a keen knowledge of trigonometric functions.
As shown in the figure on the right, let c = 90, B=α, flat distance d and hillside distance r, then the problem of secα=secB =AB/CB=r/d. ∴r=secα×d is solved.
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The second part is the application of inequality.
Inequalities commonly used in daily life are: one-dimensional linear inequality, one-dimensional quadratic inequality and average inequality. The application of the first two types of inequalities is exactly the same as that of their corresponding functions and equations, and the average inequality plays an important role in production and life.