The difference between the function differentiable in the closed interval and the function differentiable in the closed interval, why is the mean value theorem only required to be differentiable in the open interval? Why do mean value theorems only require derivability in open intervals? Closed interval is continuous, open interval is differentiable, so closed interval is differentiable? Explain why... I need a reason

The difference between the function differentiable in the closed interval and the function differentiable in the closed interval, why is the mean value theorem only required to be differentiable in the open interval? Why do mean value theorems only require derivability in open intervals? Closed interval is continuous, open interval is differentiable, so closed interval is differentiable? Explain why... I need a reason

Only the open interval is differentiable, and the endpoint does not have to be differentiable, so the mean value theorem only needs to find the open interval differentiable

It says that even if f '(x) is discontinuous, for any value C between F' (x1) and f '(x2), there must be d between X1 and X2 such that f' (d) = C. isn't this the intermediate value theorem of continuous function? It holds only when the function is continuous. Then why does it hold even if the derivative function is discontinuous?

That is to say, even if the derivative function is discontinuous, it also satisfies the intermediate value theorem. You are a graduate student of advanced mathematics, and you can know this conclusion without clear proof

Proof of integral mean value theorem: the proof of closed interval uses intermediate value theorem, but does not the intermediate value theorem of continuous function exist in open interval?

In fact, the inference of the intermediate value theorem is used. Note that the inference of the intermediate value theorem can only be established on a closed interval. You can go to the textbook

If the power of (X-2) is known to be meaningless, then the value range of X is

If the power of (X-2) is meaningless, then the value range of X is
x=2

How to read this English word,
The English word is: carries
I want phonetics and meaning

This is the third person of Carrey, specifically ['k & aelig; RIS]
Meaning: 1 transitive verb vt. (with hands, shoulders, etc.) pick, hold, carry, carry
To be carried or carried

Note that the sum of the first n terms of the arithmetic sequence {an} is Sn, if A1 = 12, S4 = 20, then S6=______ ．

The sum of the first n terms of ∵ arithmetic sequence {an} is Sn, A1 = 12, S4 = 20, ∵ A4 + A1 = 10, ∵ A4 = 192, ∵ d = 3, ∵ S6 = 6 × 12 + 6 × 52 × 3 = 48, so the answer is: 48

It is known that a, B, C, x, y, Z are unequal non-zero real numbers, and YZ / (BZ + CY) = XZ / (Cx + AZ) = XY / (ay + BX) = x ^ 2 + y ^ 2 + Z ^ 2 / A ^ 2 + B ^ 2 + C ^ 2
Verification: a + B + C = 2 (x + y + Z)
Let B / y = A / x = C / z = K

By YZ / (BZ + CY) = XZ / (Cx + AZ) = XY / (ay + BX), we divide all the numbers on the molecule, and get B / y + C / z = C / Z + A / x = A / x + B / y, that is: B / y = A / x = C / z = k is not equal to 0, then a = KX, B = KY, C = KZ is replaced by XY / (ay + BX) = x ^ 2 + y ^ 2 + Z ^ 2 / A ^ 2 + B ^ 2 + C ^ 2, and simplify to 2K = k ^ 2, so k = 2, it is easy to know a + B + C = 2 (x + y + Z)

1. 15 × 15 of 16 = () 2, 53 × 55 of 54
Simple calculation, using different methods

15 / 16 × 15
= 15 / 16 × (16-1)
＝15-15/16
= 14 and 1 / 16
53 / 54 × 55
= 53 of 54 × (54 + 1)
＝53+53/54
= 53 and 53 / 54

The volume formula divided by what equals height
It is: volume divided by what equals height
Bottom perimeter or bottom area

You think like this: because: the volume of the object = bottom area × height
So: height = volume △ bottom area

Finding n-order Taylor formula of F (x) = (1-x) / (1 + x)
What about the nth order Taylor formula with Lagrange remainder at x = 0? What I need is a process

-1+2（1-x+x^2-x^3+x^4-...)=1-2x+2x^2-2x^3+...+2(-x)^n
First, change the fraction to - 1 + 2 / (1 + x), and then follow the instructions in the book