Finding the extremum of function f (x, y) = XY (3-x-y)

Finding the extremum of function f (x, y) = XY (3-x-y)

Unconditional extremum problem
The partial derivatives of X and y are obtained respectively, and the point (x0, Y0) with partial derivative = 0 is obtained
Then, calculate the second-order partial derivatives FXX (x0, Y0) = a, fxy (x0, Y0) = B, FYy (x0, Y0) = C respectively
B ^ 2-ac > 0 (x0, Y0) is not an extreme value
B ^ 2-ac0 minimum; a

Finding the extremum of function f (x, y) = XY (x ^ 2 + y ^ 2-4)

The derivative of the extreme point must be zero, and then it can be checked

A math problem, a formula out! The first day to give you a cent, the second day to give 2 points, the third day to give 4 points, the fourth day 8 points, the fifth day 16 points, double every day, 30 days a month, the total amount of money to you!

This is an example of an equal ratio,
an=2^(n-1)
Sn=(a1-an*q)/(1-q)=2^n - 1
30 days S30 = 2 ^ 30-1

New year's day in 2002 is Tuesday, and January 1, 2003 is the day of the week
Fast!

365 / 7 = 52 + 1
Tuesday plus one day is Wednesday

All the math formulas from grade one to grade six

1. Number of copies × number of copies = total number of copies / number of copies = total number of copies / number of copies = number of copies
2. 1 times × times = several times △ 1 times = several times △ 1 times
3. Speed × time = distance △ speed = time distance △ time = speed
4. Unit price × quantity = total price / unit price = total quantity / quantity = unit price
5. Work efficiency × work time = total amount of work △ work efficiency = total amount of work time △ work time = work efficiency
6. Addend + addend = sum - one addend = another addend
7. Subtracted - subtracted = difference subtracted - difference = subtracted difference + subtracted = subtracted
8. Factor × factor = product △ one factor = another factor
9. Divisor / divisor = quotient divisor / quotient = divisor quotient × divisor = divisor
Primary school mathematics figure calculation formula
1. Square C perimeter s area a side perimeter perimeter = side length × 4 C = 4A area = side length × side length s = a × a
2. Cube V: Volume A: edge length surface area = edge length × edge length × 6 s surface = a × a × 6 volume = edge length × edge length × edge length v = a × a × a
3. Rectangle
C perimeter s area a side length
Perimeter = (length + width) × 2
C=2(a+b)
Area = length × width
S=ab
4. Cuboid
5: Volume s: Area A: length B: width H: height
(1) Surface area (L × W + L × H + W × h) × 2
S=2(ab+ah+bh)
(2) Volume = length × width × height
V=abh
5 triangles
S area a bottom h height
Area = bottom × height △ 2
s=ah÷2
Triangle height = area × 2 △ bottom
Triangle bottom = area × 2 △ height
6 parallelogram
S area a bottom h height
Area = bottom × height
s=ah
7 trapezoid
S area a upper bottom B lower bottom h height
Area = (upper bottom + lower bottom) × height △ 2
s=(a+b)× h÷2
8 round
S area C perimeter Π d = diameter r = radius
(1) Perimeter = diameter ×Π = 2 ×Π× radius
C=∏d=2∏r
(2) Area = radius × radius ×Π
9 cylinder
v: Volume H: height s; bottom area R: bottom radius C: bottom perimeter
(1) Side area = perimeter of bottom surface × height
(2) Surface area = side area + bottom area × 2
(3) Volume = bottom area × height
(4) Volume = side area △ 2 × radius
10 cone
v: Volume H: height s; bottom area R: bottom radius
Volume = bottom area × height △ 3
Total number △ total number of copies = average number
The formula of sum difference problem
(sum + difference) △ 2 = large number
(sum difference) △ 2 = decimal
The problem of sum times
Sum (multiple-1) = decimal
Decimals × multiples = large numbers
(or sum - decimal = large)
Differential multiple problem
Difference (multiple-1) = decimal
Decimals × multiples = large numbers
(or decimal + difference = large)
The problem of tree planting
1. The tree planting problem on non closed lines can be divided into the following three cases
(1) if trees are to be planted at both ends of the non closed line, then:
Number of plants = number of segments + 1 = total length △ plant spacing-1
Total length = plant spacing × (number of plants - 1)
Plant spacing = total length (number of plants - 1)
(2) if trees are to be planted at one end of the non closed line and not at the other end, then:
Number of plants = number of segments = total length △ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length △ number of plants
(3) if trees are not planted at both ends of the non closed line, then:
Number of plants = number of segments-1 = total length △ spacing-1
Total length = plant spacing × (number of plants + 1)
Plant spacing = total length (number of plants + 1)
2. The quantitative relationship of tree planting on closed lines is as follows
Number of plants = number of segments = total length △ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length △ number of plants
Profit and loss
(profit + loss) △ the difference between the two distributions = the number of shares participating in the distribution
(big profit - small profit) △ the difference between the two distributions = the number of shares participating in the distribution
(big loss - small loss) △ the difference between the two distributions = the number of shares participating in the distribution
Encounter problem
Encounter distance = speed and X encounter time
Encounter time = encounter distance △ speed and
Speed sum = encounter distance △ encounter time
Follow up questions
Pursuit distance = speed difference × pursuit time
Pursuit time = pursuit distance △ speed difference
Speed difference = pursuit distance △ pursuit time
Flow problem
Downstream velocity = hydrostatic velocity + water velocity
Countercurrent velocity = still water velocity - water velocity
Hydrostatic velocity = (downstream velocity + countercurrent velocity) △ 2
Water flow velocity = (downstream velocity countercurrent velocity) △ 2
Concentration problem
Weight of solute + weight of solvent = weight of solution
Weight of solute / weight of solution × 100% = concentration
Weight of solution × concentration = weight of solute
Weight of solute △ concentration = weight of solution
Profit and discount
Profit = selling price cost
Profit margin = profit / cost × 100% = (selling price / cost-1) × 100%
Up and down amount = principal × up and down percentage
Discount = actual selling price △ original selling price × 100% (discount < 1)
Interest = principal × interest rate × time
After tax interest = principal × interest rate × time × (1-20%)
Length Conversion
1 km = 1 000 m 1 m = 10 decimeters
1 decimeter = 10 cm 1 meter = 100 cm
1 cm = 10 mm
Area Conversion
1 sq km = 100 ha
1 ha = 10000 M2
1 square meter = 100 square decimeter
1 square decimeter = 100 square centimeter
1 sq cm = 100 sq mm
Volume (volume) product unit conversion
1 cubic meter = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cubic decimeter = 1 liter
1 cc = 1 ml
1 cubic meter = 1000 liters
Conversion of weight unit
1 ton = 1000 kg
1kg = 1000g
1kg = 1kg
Conversion of RMB units
1 yuan = 10 Jiao
1 jiao = 10 points
1 yuan = 100 points
time conversion
1 century = 100 years 1 year = December
Big month (31 days): January, March, may, July, August, October, December
Small month (30 days): April, June, September and November
The average year is 28 days in February and leap year is 29 days in February
There are 365 days in a normal year and 366 days in a leap year
1 day = 24 hours, 1 hour = 60 minutes
1 minute = 60 seconds 1 hour = 3600 seconds
Calculation formula of perimeter area volume of primary school mathematics geometry
1. Circumference of rectangle = (length + width) × 2 C = (a + b) × 2
2. Perimeter of square = side length × 4 C = 4A
3. Area of rectangle = length × width s = ab
4. Area of square = side length × side length s = A.A = a
5. Area of triangle = bottom × height △ 2 s = ah △ 2
6. Area of parallelogram = base × height s = ah
7. Area of trapezoid = (upper bottom + lower bottom) × height △ 2 s = (a + b) H △ 2
8. Diameter = radius × 2 D = 2R radius = diameter △ 2 r = D △ 2
9. Circumference of circle = circumference × diameter = circumference × radius × 2 C = π d = 2 π R
10. Area of circle = circumference × radius × radius

3 / 4 times 8 / 13 + 5 / 13 times 3 / 4 - 3 / 4 equals?

﹙3/4﹚×﹙8/13﹚＋﹙5/13﹚×﹙3/4﹚－3/4=﹙3/4﹚×﹙8/13＋5/13－1﹚=0

Xiao Wang wants to use shadow to measure the height of the tree in the campus. At a certain moment, he measured the height of the small tree to be 1.5 meters, and the shadow length was 1.2 meters. When he measured the shadow length of a big tree beside the teaching building, because the big tree was close to the teaching building, there was a part of the shadow on the wall. According to the measurement, the shadow length of the ground part was 6.4 meters, and the shadow length of the wall was 1.4 meters, so the height of the big tree was about 10 meters______ Rice

Let the height of the tree be X. according to the characteristics of parallel projection: at the same time, the height of different objects is proportional to the shadow length. We can get that the height of the tree is 1.51.2 = 1.25, and the shadow length is 6.4x − 1.4 = 11.25 = 0.8

What's 130 minus 5%? What's a number minus 5%?

5% is 0.05, so 130-0.05 = 129.95!

We know that x equals 3, y equals 1 is the solution of equation 3x minus ay equals 8, and the value of a is?

3x-Ay=8
3(3)-A(1)=8
9-A=8
A=1

37.45 divided by 8.3 is equal to?

4.5120481927710843373493975903614