What is the geometric meaning of the extremum and conditional extremum of binary function? If there is no extremum of binary function, is there necessarily unconditional extremum? Give an example There is another problem, the stationary point of binary function is not necessarily the extremum? Find an example

The extremum of binary function is a function value f (x, y) corresponding to the point (x, y) of each domain in a given definition area (smooth is a piece or a large or small area). All the function values of (x, y) are put together to form a set of ranges. Finding the maximum or minimum value of the elements in this set is called function

Given the function f (x) = 1 / 3x ^ 3-x ^ 2 + 13, find the extremum of the function

f(x)=1/3x^3-x^2+13
f'(x)=x^2-2x=0
=>X = 0, x = 2 are two extreme points
f''(x)=2x-2
=>f''(0)=-20
So x = 0 is the maximum point, and the maximum is f (0) = 13. X = 2 is the minimum point, and the minimum is f (2) = 35 / 3

3x (x - 1) = 2 (x - 1) use factorization to solve problems

3x（x—1）＝2（x—1）
3x（x—1）-2（x—1）＝0
（3x-2）(x-1)=0
x1=2/3 x2=1

Solving the equation by factoring 3x (x-4) = 2 (x-4)

3x(x-4)=2(x-4)
3x(x-4)-2(x-4)=0
（x-4）（3x-2）=0
x-4=0 3x-2=0
x1=4 x2=2/3

The greatest common factor of two numbers is 12, and the least common multiple is 60. The product of these two numbers is___ ．

12 = 2 × 2 × 3, 60 = 2 × 2 × 3 × 5, one number is: 2 × 3 × 3 = 12, the other number is: 2 × 3 × 5 × 2 = 60, the product of these two numbers is: 12 × 60 = 720

A ^ 2 + B ^ 2 = 1 AB minimum
Such as the title

A ^ 2 + B ^ 2 = 1 AB minimum
∴1=a²+b²≥2√a²b²=2ab;
∴ab≤1/2;
The maximum value is 1 / 2;
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Let the derivative of function f (x) be f '(x), and f (x) = x2 + 2xf' (1), then f '(2)=______ ．

∵ f (x) = x2 + 2xf ′ (1), ∵ f ′ (x) = 2x + 2F ′ (1), let x = 1, then f ′ (1) = 2 + 2F ′ (1), the solution is f ′ (1) = - 2, then f ′ (x) = 2X-4, so f ′ (2) = 2 × 2-4 = 0, so the answer is: 0

Twenty questions on page 39 and answers on pages 40 to 41

Page 39-40-41: abcccbaccbadbdddccaabdcba
Fill in the blanks: 42 52 51 25 33 15 4 2 99 1

Subtract two fifths from the reciprocal of two thirds and divide it by a number. The quotient is 1.5. What's the number

(3/2-2/5)/x=1.5
1.5*x=1.1
x=11/15

Calculation: - x + (2x-2) - (3x + 5)

The original formula = - x + 2x-2-3x-5 = - 2x-7