If f (x) = - 1 / 2 (x ^ 2) + bln (x + 2) is a decreasing function on (- 1, + infinity), then the value range of B is

If f (x) = - 1 / 2 (x ^ 2) + bln (x + 2) is a decreasing function on (- 1, + infinity), then the value range of B is

Theorem:
For the function f (x), if it is differentiable, then if f '(x) > = 0 is a simple increasing function, f' (x)

How many cubic meters is a cube box?

A cube box, 10 decimeters long, how many cubic meters is the volume?
10 decimeters = 1 meter
Volume: 1 × 1 × 1 = 1m3
The volume is one cubic meter
Upstairs error

Y = x & # 178; - 2aX + 3 x belongs to [- 1.3] and the range of Y is y = x & # 178; - 2x + 3 x belongs to [T.T + 1]

1. ∵ x ∈ [- 1,3], so from the symmetry we get
2a/2=1,a=1
y=x²-2x+3=(x-1)²+2
(drawing)
y∈[2,6]
2. Y = x & # 178; - 2x + 3 = (x-1) &# 178; + 2, the axis of symmetry is x = 1
① When t > 1
From the image we get y ∈ [T & # 178; - 2T + 3, T & # 178; + 2]
② When t + 1 / 2 ＞ 1 and t ≤ 1, i.e. 1 / 2 ＜ t ≤ 1
From the image we get y ∈ [2, T & # 178; + 2]
③ When t + 1 / 2 ≤ 1 and T + 1 > 1, that is, 0 < T ≤ 1 / 2
From the image we get y ∈ [2, T & # 178; - 2T + 3]
④ When t + 1 ≤ 1, that is, when t ≤ 0
From the image we get y ∈ [T & # 178; + 2, T & # 178; - 2T + 3]
To sum up

One addend is an absolute value equal to a negative rational number, and the other is the opposite of one. The sum of these two numbers is equal to（

0+(-1)= -1

What is the number of zeros of function f (x) = lgx = 2x-6

It's the intersection, two, the image solution

Let f (XY) = {a (x ^ 2 + y ^ 2), (0 ≤ x ≤ 1,0 ≤ y ≤ 1); 0, other
Let f (XY) = {a (x ^ 2 + y ^ 2), (0 ≤ x ≤ 1,0 ≤ y ≤ 1); 0, others
① Find the expectation of X, y, XY;
② Judge whether X and y are related;
③ Find cov (AX + B, y)

It is known that the function f (x) is an odd function defined on R, and f (x + 2) = - f (x). When 0 ≤ x ≤ 1, f (x) = x & # 178; + x 1) is used to find the period 2 of function f (x)
The expression of F (x) in - 1 ≤ x ≤ 0 3) to find the value of F (6.5)

F (x + 4) = f (x + 2 + 2) = - f (x + 2) = - [- f (x)] = f (x), so the minimum positive period of function f (x) is 4. When - 1 ≤ x ≤ 0, 0 ≤ - x ≤ 1, then f (- x) = - x) ^ 2 + (- x) = x ^ 2-x = - f (x), so in the expression of - 1 ≤ x ≤ 0, f (x) = - (x ^ 2-x) f (6.5) = f (2.5) = - f (0.5) = - (0.5 ^ 2 + 0.5) = - 0.75 = - 3 / 4

Find the maximum and minimum values of the following functions in a given interval
f(x)=x^3-27,x∈[-4,4]
F (x) = 3x-x ^ 3, X belongs to [2,3]

f(x)=x^3-27
f'(x)=3x^2>0
So f (x) increases monotonically over R
When x = - 4, the minimum value of F (x) is f (- 4) = - 91
When x = 4, the maximum value of F (x) is f (4) = 37
f(x)=-x^3+3x
f'(x)=-3x^2+3
Let f '(x) = 0 - > x = 1 or - 1
When x > 1, f '(x)

Given function f (x) = LG [(A-1) x ^ 2 + 2x + 1]
(1) If the domain of function f (x) is r, find the value range of real number A. (2) if the domain of function f (x) is r, find the value range of real number a

(1) (A-1) x ^ 2 + 2x + 1 > 0 always holds A-1 > 0 △ 0 △ > = 0, you can count yourself or not. If you don't understand your idea, you can ask again!
Remember to adopt it

Several mathematical problems of rational numbers
(- 1 / 6-1 / 8 + 1 / 4-1 / 12) divided by (- 1 / 48)
(- 1) 2007 power + (- 3) 2nd power multiplied by [- 2 / 9] - 4 2nd power divided by (- 2) 2nd power
2 / 5 division (- 2 and 2 / 5) - 8 / 21 times (1 and 3 / 4) - 0.5 times 2 times 1 / 2

Several mathematical problems of rational numbers
(-1/6-1/8+1/4-1/12)÷（-1/48)
=(-1/6-1/8+1/4-1/12)×（-48)
=1/6×48+1/8×48-1/4×48+1/12×48
=8+6-12+4
=6
(- 1) 2007 power + (- 3) 2nd power multiplied by [- 2 / 9] - 4 2nd power ÷ (- 2) 2nd power
=-1+9×（-2/9）-16÷4
=-1-2-4
=-7
2 / 5 △ (- 2 and 2 / 5) - 8 / 21 times (1 and 3 / 4) - 0.5 times 2 times 1 / 2
=-1/6-2/3-1/2
=-5/6-1/2
=-4/3