Let a function have a second derivative on [0,1], and | f '' (x) | ≤ m, and f (x) has the maximum value in (0,1). It is proved that | f '(0) | + | f' (1) | ≤ M Help for proof of high number

Let a function have a second derivative on [0,1], and | f '' (x) | ≤ m, and f (x) has the maximum value in (0,1). It is proved that | f '(0) | + | f' (1) | ≤ M Help for proof of high number

How can this be possible
f(x)=-x^2-10,M=2
f"(x)=-2,
The maximum value in [0,1] is - 10,
And | f (0) | + | f (1) | = 10 + 11 = 21 > M
It's not good to use parentheses, such as f (x) = - (x-0.5) ^ 2-10
f"(x)=-2,
The maximum value is - 10 in (0,1)
|f(0)|+|f(1)|=21>M

Even function f (X-2) defined on R, when x > 2, f (x) = e ^ (x-1) - 2 (E is the base of natural logarithm),
Let the real root XO of the equation f (x) = 0 belong to (k-1, K), then the value range of K is

Even function f (X-2) defined on R,
∴f(x-2)=f(-x-2),
When x > 2, f (x) = e ^ (x-1) - 2, ↑,
∴f(x)>e-2>0,
The equation f (x) = 0 has no solution
Please check the title

Dear good brothers and sisters, please help me find dozens of (note, dozens of!) rational number addition and subtraction mixed operation problems. Don't forget to add the answers. The more the better,

It is known that X and y are rational numbers, and 2x + (quadratic root 2, multiplied by Y) = y + 1 - (quadratic root 2, multiplied by x). Find the value of X and y
If the rational numbers a and B satisfy | a 4 | + B-1 | = 0, then a B =?
The letter a denotes a rational number. If ㄧ a ㄧ = - A (the absolute value of a is negative a), then a is a rational number
A. Non positive number
B. Nonnegative number
C. Negative number
D. Nonzero number

If a and B are rational numbers, discuss and represent the following numbers on the number axis
[1]|a-1|
[2]|a-b|-|a+b|

A-1 > 0 a-1a + B a-b

Given the equation 137x = 795a about X, the following statement is correct: A, ax & lt; 0, B. when x = 0, the equation has no solution C, ax ≥ 0, D, ax ≤ 0
It's an exercise for grade one······

It should be C, because if ax

a good many, a good many of, a great deal o
A good many, a good many of, a great deal of, a great deal of

Similarities:
The Chinese meaning can be translated as:
A lot; a lot
Analysis of usage:
A good / great many + countable plural
A good / great many of + pronoun objective plural
A great deal of + uncountable nouns
A great deal is used as an adverbial to indicate degree or quantity
I wish you happiness!

In the triangle ABC, the angle c = 90 & # 186;, ab = 13, BC = 5, then the value of SINB is

Because AB = 13, BC = 5, so AC = radical (AB ^ 2-bc ^ 2) = 12, so SINB = AC / AB = 12 / 13

English words or phrases expressing positional relations

On
Under, under, under, in
In the field of
To enter into
To be on top of
On top of
Below; below; below; below; below
Below; below

(the square of 99 + the square of 98 +90 square) - (89 square + 88 square +80 square)
It's a simple calculation

(the square of 99 + the square of 98 +90 square) - (89 square + 88 square +80 square)
=(99^2-89^2)+(98^2-88^2)+...+(90^2-80^2)
=(99+89)*(99-89)+(98+88)(98-88)+..+(90+80)(90-80)
=10(99+89)+10(98+88)+...+10(80+90)
=10(99++89+98+88+...+90+80)
=10*(99+80)*20/2
=17900

I've heard that you're very good. I'm looking for phrases like go out hand out give up and Chinese translation

Break out, break up, break up, break up, break up, break up, break up, break up, break up, come out, come out, come out, come out, come out, come out, come out, come out, come out, come out, come up, come up, grow up, sprout up, there are many, he said I exceeded the word limit,