Simple function problems in senior one According to the previous production and sales experience of a product manufacturer, the following statistical rules about production and sales are obtained: the total cost of each product X (100 sets) is g (x) (10000 yuan), of which the fixed cost is 28000 yuan, and the production cost of each 100 sets is 10000 yuan. The sales income R (x) (10000 yuan) satisfies R (x) = - 0.4x ^ 2 + 4.2x (0 ≤ x ≤ 5) ）11 (x ＞ 5), assuming that the production and marketing of the product are balanced (that is, all the products produced can be sold) (1) Write the analytic formula of profit function y = f (x) (profit = sales revenue total cost) (2) How many products can the factory make the most profit?

Simple function problems in senior one According to the previous production and sales experience of a product manufacturer, the following statistical rules about production and sales are obtained: the total cost of each product X (100 sets) is g (x) (10000 yuan), of which the fixed cost is 28000 yuan, and the production cost of each 100 sets is 10000 yuan. The sales income R (x) (10000 yuan) satisfies R (x) = - 0.4x ^ 2 + 4.2x (0 ≤ x ≤ 5) ）11 (x ＞ 5), assuming that the production and marketing of the product are balanced (that is, all the products produced can be sold) (1) Write the analytic formula of profit function y = f (x) (profit = sales revenue total cost) (2) How many products can the factory make the most profit?

L (x) = profit = sales revenue cost = R (x) - (x) - 2
1、 Since R (x) is a piecewise function, we need to discuss it
1. If 0 ≤ x ≤ 5, only l (x) > 0 is needed
- 0.4x & # 178; + 4.2x-0.8-x-2 > 0, the solution is: 10 is equivalent to: 10.2-x-2 > 0, the solution is: X

Senior one mathematics compulsory chapter one classic examples of function or problem solving ideas, ask for advice!
Not many points, do not understand the function, mainly parity and monotonicity of the topic

First of all, to solve the problem of function properties, we need to first find the definition field of the function. Second, we use the idea of substitution, such as f (x) = log (AX ^ 2 + BX + C) to change the quadratic function to T. then we discuss the relationship between F (- x) and f (x) and special cases for parity, such as f (0) =... When the function is odd

F (x) satisfies the condition f (x + 2) = 1F (x) for any real number X. if f (1) = - 5, then f (f (5)) = ()
A. -5B. −15C. 15D. 5

∵ f (x + 2) = 1F (x) ∵ f (x + 2 + 2) = 1F (x + 2) = f (x) ∵ f (x) is a function with a period of 4 ∵ f (5) = f (1 + 4) = f (1) = - 5F (f (5)) = f (- 5) = f (- 5 + 4) = f (- 1) and ∵ f (- 1) = 1F (− 1 + 2) = 1F (1) = - 15 ∵ f (f (5)) = - 15

It is known that the image of function y = f (x) is symmetric with respect to Y-axis and satisfies f (X-2) = ax - (A-3) x + (A-2)
1, find the analytic expression of function f (x)
2. Discuss the number of zeros of F (x) = B (B ∈ R)
3. If f (x) = B has three zeros, the function H (x) = x + 2x + C / X is known. If h (x) > 0 holds for any x ∈ [b, + ∞), try to find the value range of real number C
If f (X-2) = ax - (A-3) x + (A-2) is less squared
The third question H (x) = x + 2x + C / X is also less squared

Given that the image of function y = f (x) is symmetric about y axis and satisfies f (X-2) = ax ^ 2 - (A-3) x + (A-2) 1, the analytic expression 2 of function f (x) is obtained. The number of zeros 3 of F (x) = B (B ∈ R) is discussed. If f (x) = B has three zeros, the function H (x) = x ^ 2 + 2x + C / X is known

In order to make the function y = sinwx (W > 0) have at least 50 maximum values in the interval [0,1], then the minimum value of W is
[please explain the process in detail thankyou
The answer is 197 Π / 2 Seeking process

2K π + π / 2 = W1, let k = 49, then w = 98 π + π / 2

Some basic examples of the periodicity of functions
1. For function f (x), f (x + 2) = - f (x) holds for any x ∈ R
Proof: 4 is a period of F (x)
Variant: for function f (x), f (x + 2) = - 1 / F (x) holds for any x ∈ R
Proof: 4 is a period of F (x)
2. F (x) is an even function with period 2 defined on R. when 0 ≤ x ≤ 1, f (x) = x ^ 2, find f (3.5)

1: Proof: to prove that 4 is a period of F (x), it is equivalent to having f (x) = f (x + 4) for all x ∈ R
∵f(x)=-f(x+2)
∴f(x+2)=-f(x+4)
∴f(x)=f(x=4)
It has been proved
Variant: similarly, ∵ for all x ∈ R, f (x + 2) = - 1 / F (x), ∵,
For all x ∈ R, f (x) ≠ 0
∴f(x+4)=-1/f(x+2)=f(x)
It has been proved
2: Proof: F (x) is even function, so f (x) = f (- x)
And f (x) has a period of 2, so f (x) = f (X-2)
∴f(3.5)=f(3.5-2)=f(1.5)=f(1.5-2)=f(-0.5)=f(0.5)=0.5²=0.25

y=tan x
y=sin x
y=cos x
How to find the period of~

Just draw a picture. The formula is the absolute value sign of T = 2 π / W, which is hard to understand. This formula is used to find the absolute value of y = SiNx and y = cos X. The formula of y = TaNx is the absolute value of π / W

Sick did not go to class, the results are not done, please tell the process, the book did not write this type of Germany do not understand ah
1. Y = cos square x to find the period of function
2. U = SiNx + root sign 3 cosx to find function period
3. Given that the period of the function y = f (x) is 3, try to find the period of y = f (2x + 1)

My book has been put in school. The formula MS is k π △ Oh, Miguel = = you have the formula of COS square X in the first book, and then I won't do it = = simplify the second problem, put forward 1 / 2, = 1 / 2 (1 / 2sinx + radical 3 / 2cosx) = 1 / 2 (cos60 ° SiNx + sin60 ° cosx), double angle, I don't remember how to end it

Equation 8x2 - (m-1) x + M-7

The two real roots of 8x2 - (m-1) x + M-7 = 0 are greater than 1
Then △ > 0
According to Weida's theorem:
(m-1) / 8 = X1 + X2, i.e. (m-1) / 8 > 2 ~ so m > 17
(M-7) / 8 = X1 * X2, i.e. (M-7) / 8 > 1 ~ so m > 15
And (m-1) ^ 2-32 (M-7) > 0, we get: M25
In conclusion: M > 25

If f (x) = x square - 2aX + 5 is an increasing function in (3, + infinity), the range of a can be obtained

The abscissa of the vertex is: x = - (- 2A) / 2 = a
When the vertex is on the left side of x = 3, the problem condition is satisfied,
So: a ≤ 3