Given the function FX = - 3 / x, it is proved by definition that FX is an increasing function in the interval (negative infinity, 0)

Given the function FX = - 3 / x, it is proved by definition that FX is an increasing function in the interval (negative infinity, 0)

Let X1 and X2 belong to (negative infinity, 0), and X1 < x2
Then f (x1) - f (x2)
=-3/x1-（-3/x2）
=3/x2-3/x1
=3(x1-x2)/x1x2
From X1 < X2, x1-x2 < 0
From x1, X2 belong to (negative infinity, 0), we know that x1x2 > 0
That is, 3 (x1-x2) / x1x2 < 0
So f (x1) - f (x2) < 0
That is, FX is an increasing function in the interval (negative infinity, 0)

It is proved that the function f (x) = 1-2 / X is an increasing function on the interval (1, + infinity)

f(x)=2/(1-x)
prove
Suppose 1

It is known that the image of function f (x) = x3-ax2 + BX + C is curve C. (1) if there is a point P on curve C, and the tangent of curve C at point P is parallel to the X axis, find the relationship between a and B; (2) if function f (x) can get the extremum at x = - 1 and x = 3, find the value of a and B; (3) under the condition of (2), f (x) < 2C is constant at x ∈ [- 2,6], find the value range of C

(1) Let f '(x) = 3x2-2ax + B and the tangent point be p (x0, Y0), then the slope of the tangent line of the curve y = f (x) at P K = f' (x0) = 3x02-2ax0 + B. from the problem, we know that f '(x0) = 3x02-2ax0 + B = 0 has a solution, that is, A2 ≥ 3B

63 26 7 0 - 2 - 9 (- 28) for regularity

63=(4^3)-1
26=(3^3)-1
7=(2^3)-1
0=(1^3)-1
-2=(-1^3)-1
-9=(-2^3)-1
(-3^3)-1=-27-1=-28

What is the derivative of "x to the x power of X"

A:
y=x^x
Take natural logarithm on both sides:
lny=xlnx
Two side derivation:
y' /y=lnx +1
y'=y(1+lnx)
y'=(x^x)(1+lnx)
So:
The derivative is (x ^ x) (1 + LNX)

What is nine tenths minus (one fifth minus one tenth)

Four fifths

Solution equation: 5m-4 of 2m-4 = 2m-6 + 1 of 5-2

(5m-4)/2(m-2)=(2m+5)/3(m-2)-1/2
3(5m-4)=2(2m+5)-3(m-2)
15m-12=4m+10-3m+6
14m=28
m=2
Test: M = 2 is the increasing root
Ψ M = 2 is the solution of the equation

When a bottle is filled with water, the total mass of water and bottle is 120g. When it is filled with alcohol, the total mass of alcohol and bottle is 100g. What is the mass of alcohol in the bottle

M water + m bottle = 120 ------- (1)
M wine + m bottle = 100 ------- (2)
It's the same volume
So v = m water / P water = m wine / P wine
Because P water / P wine = 1 / 0.8 = 5 / 4
So m water / M wine = 5 / 4
Substituting (1) formula, m liquor = 80g

7 out of 12, 5 out of 32 and 9 out of 48, please divide them and compare their sizes
How much is 39 out of 52? I feel like I can't make an appointment, but why does it appear on my paper?

The denominators of the three fractions are 12, 32 and 48
Their least common multiple is 96
7 out of 12 = 56 / 96
5 out of 32 = 15 / 96
9 / 48 = 18 / 86
So 7 out of 12 > 9 out of 48 > 5 out of 32
39 out of 52 divide it into 3 / 4 (the numerator and denominator divide by 13 at the same time)

3.75 * 0.5-2.75/2 6.3/1.8 9.5 / (1.9 / 8) (7.7 + 1.54) / 0.7 (11.7-9.9) / 0.9 calculated by simple method

3.75*0.5-2.75/2=3.75/2-2.75/2=（3.75-2.75）/2=1/2=0.56.3/1.8=3.59.5/（1.9/8）=9.5/1.9*8=5*8=40（7.7+1.54）/0.7 =7.7/7+1.54/7=1.1+0.22=1.32（11.7-9.9）/0.9=11.7/0.9-9.9/0.9=13-11=2