Given that f (x) = root sign (AX ^ 2-ax + 4) holds for any x constant, find the value range of A

Given that f (x) = root sign (AX ^ 2-ax + 4) holds for any x constant, find the value range of A

(1) When a = 0, the number of square root is 4
(2) When a ≠ 0, ∵ holds ∵ a > 0 for any x constant and △ = a ^ 2-16a

It is known that f (x) is equal to AX minus ax plus 4 under the root sign

(1) When a = 0, the number of square root is 4
(2) When a ≠ 0,
∵ holds for any x constant
A > 0 and △ = a ^ 2-16a

Let f (XY, X-Y) = x & # 178; + Y & # 178;, then f (x, y) =?
Let f (X-Y, x + y) = XY, find f (x, y) these two questions are the same question type

f(xy,x-y)=x²+y²=-2xy+(x-y)^2
So f (x, y) = - 2x + y ^ 2
f(x-y,x+y)=xy=1/4[(x+y)+(x-y)][(x+y)-(x-y)]
f(x,y)=1/4(y+x)(y-x)=1/4(y^2-x^2)

Let x (x-1) - (X & # 178; - y) = - 2, find the value of (X & # 178; + Y & # 178;) / 2-xy

x(x-1)-(x²-y)=-2
x²-x-x²+y=-2
x-y=2
（x²+y²）/2-xy=(x²+y²-2xy)/2
=(x-y)²/2
=2

Let f (x, y) = ∫ 0 product to √ XY [e ^ ({- 2T} ^ 2) DT (x > 0, Y > 0)] and find DF (x, y)
Let the partial derivative of Z = f (x, y) exist and be bounded in the open interval D. It is proved that z = f (x, y) is continuous in D

1. Is the integrand e ^ (4T ^ 2)?
df(x,y)=af/ax*dx+af/ay*dy
=0.5E ^ (4xy) radical (Y / x) DX + 0.5E ^ (4xy) radical (x / y) dy
2. Let (a, b), | f (a + DX, B + dy) -- f (a, b)|

Let (x-1) (y + 1) = 3 and XY (X-Y) = 4;

XY + X-Y = 4
Consider xy and X-Y as a whole, xy = 2, X-Y = 2
X & # 178; + Y & # 178; = (X-Y) square + 2XY = 8

The total utility function is u = XY, the price of X is 2 yuan, and the price of Y is 3 yuan
The total utility function is u = XY, the price of X is 2 yuan, and the price of Y is 3 yuan
(1) How to choose X and y? Is it most effective?
(2) What are the marginal and total utility of money
(3) If the price of x increases by 40% and the price of Y remains unchanged and the utility remains unchanged, how much should his income be?
Note that the third answer is 40%, not 44% on the Internet

1)
2X+3Y=120
Y=40-2X/3
U=XY=X(40-2X/3)
=-2X^2/3+40X
=-2/3(X-30)^2+600
X=30,Y=20
U=600
2)
U=(X+1)(Y+1)-XY
=X+Y+1
U=XY
X=0,Y=0
U=0
0

Western Classic: a person earns 120 yuan a week and spends all his money on X and Y commodities. His utility function is u = XY, PX = 2 yuan, py = 3 yuan
How many units of X and y will he buy for maximum utility?
(2) What are the marginal utility and the total utility of money?
(3) If the price of x increases by 44% and the price of Y remains unchanged, how much more income must be increased to keep its original utility level?
Ask for detailed answers
Solution: (1) from u = XY, we get MUX = y, muy = x, according to the consumer equilibrium condition, we get y / 2 = x / 3
Considering that the budget equation is 2x + 3Y = 120
The solution is x = 30, y = 20
(2) The marginal utility of money λ = MUX / PX = Y / PX = 10
Total utility Tu = xy = 600
(3) After the price increase, PX = 2.88, the new consumer equilibrium condition is Y / 2.88 = x / 3
From the meaning of the title, we know that xy = 600, the solution is x = 25, y = 24
Put it into the budget equation M = 2.88 × 25 + 3 × 24 = 144 yuan
Δ M = 144-120 = 24 yuan
Therefore, in order to maintain the original level of utility, the income must be increased by 24 yuan
Please explain: why "from u = XY, MUX = y, muy = x"

This is the formula for solving the marginal utility. The marginal utility is the total utility that the consumer increases by adding a unit of consumption of a certain commodity, that is, Mu = DTU / DX, which is the inverse of the total utility. The total utility function is u = XY, and the derivative of commodity x is the marginal effect of commodity X

3. A person with a monthly income of 120 yuan can spend on X and Y commodities, and his utility function is u = XY, PX = 2 yuan, py = 4 yuan. Ask: (1) how many units of X and y will he buy in order to obtain the maximum utility? (2) what are the marginal utility and total utility of money? (3) if the price of x increases by 44%, and the price of Y remains unchanged, how much more must his income increase in order to maintain the original utility level?
(3) The new equilibrium condition is: and u = xy = 450
Therefore, the income must be increased to, that is, the income can be increased by 24
Maintain the original level of total utility
Please explain

MUX / PX = muy / py = > y / 2 = x / 4. (1) 2x + 4Y = 120. (2) from (1) (2) we get x = 30, y = 15, marginal utility of money = MUX / PX = 7.5, total utility = xy = 450xy = 450. (3) MUX / PX = muy / py = > y / 2.88 = x / 4. (4) from (3) (4) we get x = 25, y = 18m = 120m '= 25 * 2.88 + 18 * 4 = 144, increase income

The utility function is u = XY, PX = 2 yuan, py = 3 yuan. Find (1) how many units of X and y will he buy in order to get the maximum utility? (2) how much is the marginal utility and the total utility of money? (3) if the price of X increases by 44%, and the price of Y remains the same, how much does his income have to increase in order to maintain his original utility level? (8 points)

Here's the right answer
Let's start with the standard algorithm
1)
Partial U / partial X / partial U / partial y = - dy / DX = 2 / 3, so y / x = PX / py, = > y = 30, x = 20
The rest will be gone, right?
Besides, this kind of equation of u = XY type X, y is homogeneous, as long as we use the mean inequality, we can easily get the answer