Hua Luogen said that mathematical analysis should be combined with number and type, and the geometric meaning of partial derivative of binary function should be understood too much in the book

You can imagine a binary function as a film or a surface (such as a sphere) in a three-dimensional space, and any point on the surface can always make a tangent plane (that is, there is only one intersection point between the surface and the surface). On this tangent plane, starting from the tangent point, make two lines parallel to xoz plane and YOZ plane respectively, Then these two lines are the geometric meaning of the corresponding partial derivatives, that is, the tangent direction parallel to xoz or YOZ

Given the square of FX = - x + ax + 2, X ∈ [- 1,1]. (1) if the maximum value of FX is g (a), find the expression of G (a). (2) f (x) max = 1
Find the value of A

Axis of symmetry x = A / 2, opening downward
Classification discussion: (1) when a / 2 & lt; - 1, i.e. a & lt; - 2, [- 1,1] is on the right side of the symmetry axis, so it is a monotone decreasing interval, so when x = - 1, there is a maximum value of 1-A
(2) When - 1 & lt; = A / 2 & lt; = 1, that is - 2 & lt; = A & lt; = 2, the axis of symmetry is in the interval, so there is a maximum value of 2 + A ^ 2 / 2 on the axis of symmetry
(3) When a / 2 & gt; 1, i.e. a & gt; 2, the interval [- 1,1] is on the left side of the symmetry axis, so the interval is monotonically increasing, so there is a maximum value of 1 + a when x = 1
So g (a) is a piecewise function
g(a)={1-a,a<-2
.{2+a^2/4,-2<=a<=2
.{1+a,a>2
(2) The maximum value of F (x) is 1. Find the value of A
According to the first question, if the maximum value of F (x) is g (a), then
When a & lt; - 2, let 1 - a = 1, then a = 0, not satisfied
When - 2 & lt; = A & lt; = 2, let 2 + A ^ 2 / 4 = 1, then a ^ 2 = - 4, no solution
When a & gt; 2, let 1 + a = 1, then a = 0
So such a does not exist

Why can we use discriminant to judge the root of quadratic equation with one variable

∵ ax & sup2; + BX + C = 0 (a, B, C are real numbers, a ≠ 0) ∵ a (X & sup2; + (B / a) x) + C = 0A (X & sup2; + 2 (B / 2a) x + (B / 2a) & sup2; - (B / 2a) & sup2;) + C = 0A (x + B / 2a) & sup2; - A (B / 2a) & sup2; + C = 0A (x + B / 2a) & sup2; - B & sup2; / 4A + C = 0A (x + B / 2a) & sup2; = B & sup2; / 4a-c

How to calculate a and B in linear regression equation

We can use the intercept function of Excel to get intercept B, slope function to get slope a

[ask a question about definite integral ~]
Let f (x) be continuous on (- ∞, + ∞) and satisfy the following conditions: ∫ (lower limit is 0, upper limit is x) f (x-u) e ^ u Du = SiNx, X ∈ (- ∞, + ∞), find f (x)

(upper limit x lower limit 0) f (x-u) DX = SiNx / e ^ u, then f (x-u) = - cosx / e ^ u, let x = x-u, substitute f (x) = - cos (x + U) / e ^ U

Answers to the first semester mathematics exercise book of grade 6 in Yangpu District, Shanghai
1) The area of rectangle is two fifths square meter, and the area of shadow is two fifths of that of rectangle
Xiao Jie reads a 150 page book. If he reads another 10 pages, he will read three fifths of the whole book
How many pages does Xiao Jie read in this book?
If he has to return the book after seven days, how many pages does Xiao Jie read every day?
What is the average number of pages read in the last seven days
3) In the third quarter, Xiaoli's monthly electricity consumption is 14 / 15 of that of the previous month. It is known that the electricity consumption in September is 225 kwh. How much more kwh is used in September than in July? If the electricity charge of 1 kwh is 0.61 yuan, how much less will Xiaoli pay in July than in September?
4) For a two-thirds fraction, add the same positive integer to its numerator and denominator at the same time to get a new fraction. Is this fraction equal to two-thirds? What kind of conclusion can you get?
To be able to solve one of the problems is OK! Of course, the best solution!

The area of rectangle is two fifths square meter, and the area of shadow is two fifths of that of rectangle
Two fifths x two fifths
= 4 / 25 (M & sup2;) a: 4 / 25 (M & sup2;)
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Xiao Jie reads a 150 page book. If he reads another 10 pages, he will read three fifths of the whole book
Suppose you have read x pages. Ten out of 150 = one in 15
(x + 10) △ 150 = two fifths A: one fifteenth of the book
X = 80 A: eight out of fifteen
150-80 = 70 (page) 70 △ 7 = 10 (page) answer: read 10 pages every day
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In the third quarter, Xiaoli's monthly electricity consumption is 14 / 15 of that of the previous month. It is known that the electricity consumption in September is 225 kwh. How much more kwh is used in September than in July? If the electricity charge of 1 kwh is 0.61 yuan, how much less will Xiaoli pay in July than in September?
225 × 14 / 15 = 210 (degree)
210 × 14 / 15 = 196 (degree)
225-196 = 29 (degrees)
29 × 0.61 = 17.69 yuan
A: September uses 29 degrees more electricity than July
A: 17.96 yuan less
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For a two-thirds fraction, add the same positive integer to its numerator and denominator at the same time to get a new fraction. Is this fraction equal to two-thirds? What kind of conclusion can you get?
Not equal. Add two-thirds of the numerator and denominator and add 1 to make three-quarters
Add four fifths to the numerator and denominator
Add three sixths to all
And so on
The later number is three-thirds of the original
It's getting closer to 1
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We've finished and approved these questions. You can copy them boldly. I'm all right. As long as you don't lazy, copy all the words, you'll be right. Don't come to me
It's tiring to type so many words. You should be kind
Finally, give me the flag. I'm very tired=|||
Good luck
PS: Xiaobai, don't steal

If C (− 3,0), D (3,0) and m are the moving points on the ellipse x24 + y2 = 1, then the minimum value of 1 | MC | + 1 | MD | is______ ．

Let C and d be the focus of the ellipse x24 + y2 = 1, so | MC | + | MD | = 2A = 4, so | MC | ·| MD | ≤ (| MC | + | MD |) 2 = 22 = 4, if and only if | MC | = | MD |, take the equal sign, that is the coordinate of point M

A formula calculation for grade five
2 / 3 (two-thirds) of a number is 1 / 5 (one-fifth) less than itself. What is the number?

1/5÷（1－2/3）＝1/5÷1/3 ＝3/5

The piecewise function f (x) = the square of X + 1 (x is greater than or equal to 0) f (x) = 1 (x is less than 0) makes f (1-x) greater than the value range of X of F (2x)
I hope we can clarify the criteria of classification discussion

From the title,
{ x²+1,x≥0
f(x)={
{ 1,xf(2x)
There are two cases
When 1.2x ≥ 0,
To satisfy 1-x & # 178; > 2x
Solution
x∈[0,√2-1)
2.2x0
x∈(-1,0)
in summary,
x∈(-1,√2-1)

What is the main content of space-time view of special relativity put forward by Einstein?

Relativity is a basic theory about space-time and gravity, which was founded by Einstein. It is divided into special relativity (special relativity) and general relativity (general relativity)

Hua Luogen said that mathematical analysis should be combined with number and type, and the geometric meaning of partial derivative of binary function should be understood too much in the book