A math problem: on the number axis, point a means negative 10, point B means positive 14 1. Please divide line AB into six equal parts to get C, D, e, F and g respectively, and then write down the numbers they represent? 2. Please divide the line AB into four equal parts to get the points h, m and N respectively, and then write down the numbers they represent?

C.-6 D.-2 E.2 F.6 G.10
H.-4 M.2 N.8

The absolute value of X + 1 is equal to two in geometric sense

The distance from the number x to - 1 is equal to two units
X = 1 or - 3

The absolute value of (x-1) + the absolute value of (x-3) > 4. How to solve this problem by combining numbers and shapes in geometric sense?
The book is too brief to understand

X-1 + x-3 & gt; 4, it can be understood that the sum of the distances from the unknown point x to point 1 and to point 3 on the number axis is greater than 4, that is, it can not be too close to 1 and 3 on the number axis
Because the absolute value can only be positive, when we calculate the absolute value of a negative number, we need to change it to positive again, so we usually calculate the absolute value of an equation with unknowns by sections
The inequality solution of this example can be explained by referring to the figure below
(1) When the unknown number falls in the region of X ≥ 3, the expression of the absolute value of the two demands in the inequality is positive. As shown in the figure, when the number axis point 3 is calculated to the right, the absolute value sign can be directly removed, and the inequality becomes & nbsp; (x-1) + (x-3) & gt; 4, that is, 2x & gt; 0. The solution set obtained is compared with the region restriction condition of the unknown number (x ≥ 3) to determine the actual solution set;
(2) When the unknown number falls in the region of X ≤ 3, the two expressions in the inequality are both negative, and the range of X is shown in the left part of the number axis point 1 on the graph. To find the absolute value, the internal negative sign must be changed to positive, and the inequality becomes & nbsp; - (x-1) - (x-3) & gt; 4, that is - 2x + 4 & gt; 4 & nbsp;. Similarly, the solution set obtained is compared with the regional restriction condition of the unknown number (x ≤ 1) to determine the actual solution set;
(3) When the unknown number falls in the 1 & lt; X & lt; 3 region, such as the interval between point 1 and point 3 on the number axis in the figure above, the expression of the absolute value of the two terms in the inequality is positive and negative, (x-1) & gt; 0, (x-3) & lt; 0, and the inequality becomes & nbsp; X-1 - (x-3) & gt; 4, i.e. 2 & gt; 4, which is impossible, that is, X is not allowed to fall in the interval; it shows that the distance between the point x on the number axis and the two points 1 and 3 is too close, It can't satisfy the inequality requirement

Geometric meaning of absolute value
|x+2|+|x-1|

Judge the positive and negative value of x value in each absolute value, remove the absolute value sign by section, and then calculate to get the maximum and minimum value
If x is greater than or equal to 2 / 3, the first term is positive, the second term is also positive, and f (x) = X-6 (x > = 2 / 3) minimum value - 16 / 3
Similarly, - 2 - 16 / 3
x8
That is to say, f (x) has a minimum value of - 16 / 3 and a maximum value of infinity

|X-3 | + | x + 2 | = 7, x =?

|X-3 | is the distance from X to 3
|X + 2 | is the distance from X to - 2
The sum of the two distances should be equal to 7
So draw a number axis and find that when the point is - 3, the distance to - 2 is 1, the distance to 3 is 6, and the sum is 7
At 4, the distance to - 2 is 6, the distance to 3 is 1, and the sum is 7
So x = - 3,4

According to the geometric meaning of absolute value, if | X-2 | 3 is known, then the range of X is

-3

What is the difference between integral and differential in geometric sense

Differential is to find the slope of the curve, integral is to find the area of irregular area (geometric interpretation)

How to understand the geometric meaning of differential

As shown in the figure, the geometric meaning of the differential dy of y = f (x) with respect to △ x (= DX) at x0 is "red line segment" [= F & # 39; (x0) DX, which can also be the increment on the tangent at x0.]

As for the geometric meaning of differential, we usually see the following expression:
Let Δ X be the increment of point m on the curve y = f (x) on the abscissa, Δ y be the increment of point m corresponding to Δ x on the ordinate, and Dy be the increment of point m tangent corresponding to Δ x on the ordinate, We can use tangent line segment to replace curved line segment approximately. "But some books say that" when | Δ x | is very small, | Δ y-dy | is much smaller than | Δ y | (higher order infinitesimal), ". Is | Δ y-dy | much smaller than | Δ y |" or | Δ y-dy | much smaller than | Δ x | "what is the difference between these two statements?

The other sentence is wrong!
When | Δ y-dy | is a higher order infinitesimal hour of | Δ y | it is equivalent to | dy | - > | Δ y |, when | Δ x | - > 0|
So tangent line segment can be used to replace curve segment approximately

Geometric meaning of function differentiation at one point

The geometric meaning of the differential function is: the increment K Δ X of the tangent ordinate. Of course, in the binary function, the geometric meaning needs to be expanded, z = f (x, y). This is the increment Z of the vertical coordinate of the tangent plane at that point in the three-dimensional plane