We know that the function is an odd function on f (x) = AX3 + CX + D. when x = 1, we take the extremum - 2 and find the monotone interval and maximum of F (x)

We know that the function is an odd function on f (x) = AX3 + CX + D. when x = 1, we take the extremum - 2 and find the monotone interval and maximum of F (x)

Because the odd function f (- x) = - f (x) - ax ^ 3-cx + D = - ax ^ 3-cx-d2d = 0d = 0, f (x) = ax ^ 3 + CX is derived from F '(x) = 3ax ^ 2 + C. according to the meaning of F (1) = a + C = - 2F' (1) = 3A + C = 0, we get a = 1 C = - 3, so f (x) = x ^ 3-3xf '(x) = 3x ^ 2-3 = 3 (x + 1) (x-1) according to f' (x), it is not difficult to find that f (x) is in (negative infinity, - 1

The odd function f (x) = ax ^ 3 + BX ^ 2 + CX + D has an extreme value of - 2 when x = - 1. (1) find the analytic expression of F (x) (2) find the monotone interval of F (x)
Why is the odd function B = D = 0? Is that a question?

Since it is an odd function, there should be no even degree term
b=d=0.
So: F (x) = a * x ^ 3 + Cx
Derivation, f (x) '= 3A * x ^ 2 + C
Because the extremum - 2 is obtained when x = - 1, so:
f(-1)'=0,f(-1)=-2.
So:
3a+c=0,
-a-c=-2.
So:
a=-1,c=3.
So:
(1)
f(x)=-x^3+3x.
(2)
f(x)'=3ax^2+c=-3x^2+3.
Let f (x) '= 0, get x = 1 or x = - 1,
So:
The function is monotonically decreasing on (- infinity, - 1],
The function is monotonically ascending on (- 1,1),
The function is monotonically decreasing on (1, + infinity)

Given the function f (x) = x ^ 3 + BX ^ 2 + CX + 2, we can get the extremum-1 at x = 1 and find the monotone interval of F (x)

Get the extremum - 1 at x = 1
f'(1)=3*1^2+2b*1^2+c=0
f(1)=1+b+c+2=-1
b=1,c=-5
f'(x)=3x^2+2x-5
Monotone interval increasing f '> 0, [1, + ∞) (- ∞, - 5 / 3]
Minus, f '

X square + 4x-4 = 0

x²+4x=4
x²+4x+2²=4+2²
﹙x﹢2﹚²=8
x﹢2=±√8
x+2=±2√2
∴x1=2√2-2
x2=-2√2-2

3 / 4 times 8 / 16 minus 3 / 10 divided by 9 / 4

3 / 4 times 8 / 16 minus 3 / 10 divided by 9 / 4
=3 / 8 - 27 / 40
=15 out of 40-27 out of 40
=- 22 out of 40
=-11 out of 20

A cuboid wood is 3 meters long. Now, after sawing the wood into 4 sections, the surface area increases by 48 square decimeters. The volume of the cuboid wood is 3 meters______ Cubic decimeter

3 meters = 30 decimeters, 48 △ 6 × 30, = 8 × 30, = 240 (cubic decimeters). Answer: the volume of this wood is 240 cubic decimeters

7 / 14 * 1 / 5 + 7 / 24 divided by 5 + 1 / 5

7 / 14 * 1 / 5 + 7 / 24 divided by 5 + 1 / 5
=(1/5)×(7/14+7/24+1)
=(1/5)×(43/24)
=43/120;
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It is proved that (n + 1) 2005 + n2005 + (n-1) 2005 - 3n-3n is divisible by 10

Certification:
Because 2005 = 4 * 501 + 1
So the mantissa of (n + 1) ^ 2005 is the same as that of (n + 1) ^ 1, that is, the mantissa of (n + 1) ^ 2005 is n + 1
The mantissa of n ^ 2005 is the same as that of n ^ 1, that is, the mantissa of n ^ 2005 is n
The mantissa of (n-1) ^ 2005 is the same as that of (n-1) ^ 1, that is, the mantissa of (n-1) ^ 2005 is n-1
So the mantissa of (n + 1) ^ 2005 + n ^ 2005 + (n-1) ^ 2005 is n + 1 + N + n-1 = 3N
3n-3n = 0, that is, the mantissa of (n + 1) ^ 2005 + n ^ 2005 + (n-1) ^ 2005-3n is 0
So the proposition of divising 10 is proved

Simple calculation of 18.6 × 99

18.6×99
＝18.6×（100-1）
＝18.6x100-18.6
=1860-18.6
=1841.4

Proof: A & # 178; + B & # 178; ≥ 2Ab
Prove that a & # 178; + B & # 178; ≥ 2Ab

A & # 178; + B & # 178; - 2Ab difference comparison method
=a²-2ab+b²
=(a-b)²
>=0
∴a²+b²>=2ab