Function and its derivative function f (x) = - x ^ 3 + ax ^ 2-4 (a ∈ R) f '(x) is its derivative function Function f (x) = - x ^ 3 + ax ^ 2-4 (a ∈ R) 1. When a = 2, for any m ∈ [- 1,1], n ∈ [- 1,1], find the minimum value of F (m) + F '(n) 2. If there exists x0 ∈ (0, + ∞) and f (x0) > 0, the value range of a is obtained

Function and its derivative function f (x) = - x ^ 3 + ax ^ 2-4 (a ∈ R) f '(x) is its derivative function Function f (x) = - x ^ 3 + ax ^ 2-4 (a ∈ R) 1. When a = 2, for any m ∈ [- 1,1], n ∈ [- 1,1], find the minimum value of F (m) + F '(n) 2. If there exists x0 ∈ (0, + ∞) and f (x0) > 0, the value range of a is obtained

（1）f(m)=-m³+2m²-4,f’(n)=-3n²+4n.
When m ∈ [- 1,0], f '(m) is 0, so f (m) increases on [0,1]. Thus, when m = 0, the minimum value of F (m) is - 4
On the other hand, f '(n) = - 3N & sup2; + 4N = - 3 (n-2 / 3) & sup2; + 4 / 9, it is easy to know that when n = - 1, the minimum value is - 7
Therefore, when m = 0; n = - 1, f (m) + F '(n) is the minimum, and the minimum value is - 11
(2) Since f (0) is a fixed value - 40, that is, 2A & sup3; - 6A & sup2; + 270, 2A & sup3; - 6A & sup2; + 27 > 0 is always true
To sum up, a has no solution, that is, a ∈Φ

If f (x), G (x) are differentiable functions on R, and f '(x) is greater than or equal to G' (x) for any x belonging to [a, b], then
For any x belonging to [a, b], there is a constant
(A) F (x) + F (a) greater than or equal to G (x) + G (a)
(B) F (x) + G (a) greater than or equal to G (x) + F (a)
(C) F (x) + F (b) is greater than or equal to G (x) + G (b)
(D) F (x) + G (b) greater than or equal to G (x) + F (b)

F '(x) - G' (x) is always greater than or equal to 0
It is shown that f (x) - G (x) increases monotonically
So when x ∈ [a, b]
f(x)-g(x)≥f(a)-g(a)
f(x)+g(a)≥f(a)+g(x)
For comparison, choose B!
If you think the explanation is not clear enough, please ask
I wish: progress in learning!

He stayed here one and a half day

days

What is the difference between one and a half days and one and a half apples?
One and a half days _____ all I can spare.Don 't forget the apples.One and a half apples _____ left on the table.
A.is;are
B.are;is
C.was;were
D.were;was

One and a half years is a long time for me

-___ one and a half days enough for the painting to be finished?
-I don't think it's enough and only after __ go on with it.
A Is ;will he recover he can B Are;he recovers can he
C Are;he recovers he can D Is;he recovers can he
The main problem is BD. why use is instead of are?

This is mainly because it regards one and a half days as a noun subject. Is one and a half days enough to complete the painting

One and a half hours a day

No, because how of is about frequency

Is there any difference between one month and a half and one and a half month?
One hour and a half and one and half an hour, which is right?

There is no difference between one month and a half and one and a half month
One hour and a half!

One and a half apples is written in the grammar book?

It's a grammar
This sentence can be translated into one and a half apples, one and a half is one plus half, less than two, so when we use is to use are for two or more hard understanding, we have to understand it in this way. This is what you need to remember, that is to use it in this way. There is no reason, just like we don't know why words are such a combination

The usage of one and a half
One and a half apples is left on the plate!
In fact, I think it's wrong, but the teacher's paper says is. Are you sure it's wrong?

Your sentence isn't correct!The accepted version should be:
One and a half apples are left...

What does the word half mean? What's the plural?

Half means half, and the plural is half
half an apple
one and a half hours
cut the apple in halves