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.
Next, I will tell you one thing I experienced personally.
With the diversification of preferential forms, "selective preferential treatment" is gradually adopted by more and more operators. Once, I went shopping in a supermarket in Wu Mei, and an eye-catching sign attracted me, which said that buying teapots and teacups could be discounted, which seemed rare. What's even more strange is that there are actually two preferential ways: (1) sell one for one (that is, buy a teapot and get a teacup); (2) 10% discount (that is, 90% of the total purchase price). There is also a prerequisite: buy more than three teapots (teapot 20 yuan/one, teacup 5 yuan/one). From this, I can't help thinking: Is there a difference between these two preferential measures? Which is cheaper? I naturally thought of the functional relationship, and decided to apply the knowledge of functions I learned to solve this problem by analytical methods.
I wrote on the paper:
Suppose a customer bought X cups and paid Y yuan (x>3 and x∈N), then
Pay y1= 4× 20+(x-4 )× 5 = 5x+60 according to the first method;
Use the second method to pay y2=(20×4+5x)×90%=4.5x+72.
Then compare the relative sizes of y 1y2.
Let d = y1-y2 = 5x+60-(4.5x+72) = 0.5x-12.
Then there will be a discussion:
When d>0, 0.5x-12 >; 0, namely x & gt24;
When d=0, x = 24.
When d < 0, x
To sum up, when buying more than 24 teacups, method (2) saves money; When only 24 pieces are purchased, the prices of the two methods are equal; When the purchase number is only between 4 and 23, the method (1) is cheap.
Visible, using a function to guide shopping, that is, exercise the mathematical mind, divergent thinking, but also save money, put an end to waste, really kill two birds with one stone!
Second, 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.
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. Below, I mainly talk about the application of mean inequality and mean value theorem.
In production and construction, many practical problems related to optimization design can usually be solved by applying mean inequality. Although the author has not personally experienced the application of mean inequality knowledge in daily life, it is not difficult to find that mean inequality and extreme value theorem can usually have the following two poles from news media such as TV newspapers and the application problems we have done.