The monotonicity of ｛ = ｛ - x

The monotonicity of ｛ = ｛ - x

A:
y=½√（-x²+3x-2）
y=½√[-(x-3/2)²+1/4]
Parabola g (x) = - (x-3 / 2) &# 178; + 1 / 4 > = 0, opening downward, axis of symmetry x = 3 / 2
One
The smallest natural number is______ The smallest odd number is______ The smallest prime number is______ The smallest sum is______ .
The minimum natural number is 0, the minimum odd number is 1, the minimum prime number is 2, and the minimum composite number is 4. So the answer is: 0; 1; 2; 4
Monotonicity of derivative
The first step is to derive the function
Step 2: let the derivative function be greater than 0, the range of solution x, then the (strictly) increasing interval of the function is obtained
Let the derivative function be less than 0 and the range of solution x, then the (strictly) decreasing interval of the function is obtained
explain:
If the derivative function is equal to or greater than 0, the solution is the non decreasing interval, or the general increasing interval;
If the derivative is less than or equal to 0, the solution is the non increasing interval or the general decreasing interval
Write 4 groups of Coprime numbers as required. (write 4 groups for each question) 1. Two are prime numbers. 2. Two are composite numbers. 3. One is prime number and the other is composite number
1. Both are prime numbers: 2 and 3, 5 and 7, 11 and 13, 17 and 19
All prime numbers are coprime
2. Both are composite numbers: 4 and 9, 8 and 15, 4 and 15, 9 and 16
3. One is prime and the other is composite: 3 and 4, 5 and 6, 7 and 8, 10 and 11
(adjacent numbers are reciprocal)
For any x ∈ R, the derivative of function f (x) exists. If f '(x) < f (x) and a > 0, then the following statement is correct
A f （a ）＞e ^a ·f （x ）
B f （a ）＜e ^a ·f （x ）
C f （a ）＞f （0）
D f （a ）＜f （0）
f'(x)
Write coprime numbers: two odd numbers are coprime numbers: (); two composite numbers are coprime numbers: (); a prime sum is a composite number is coprime numbers: ()
5,7； 4,9; 2,7
Find the derivative of function y = f (COS & # x) (where f (x) is differentiable)
y=f(cos²x)
y'=f'(cos²x)*(cos²x)'
=f'(cos²x)*(-2sinxcosx)
Write three pairs of Coprime numbers: 1. Two numbers are prime numbers (); 2. Two numbers are composite numbers (); 3. One prime number and one composite number ()
1. Two numbers are prime numbers (2 and 3); two numbers are composite numbers (8 and 9); three numbers are prime numbers and composite numbers (3 and 4)
1. Both numbers are prime numbers (3 and 5);
2. Both numbers are combined (14 and 15);
3. A prime number, a composite number (7 and 22)
Two numbers are prime numbers (27); 2. Two numbers are composite numbers (49); 3. One prime number and one composite number (29)
1.(2,3) 2.(4,6) 3.(2,4)
1--2 3
2--4 9
3--2 9
Find the derivative of function f (x) = (1 + x) &# 178; (1-x) &# 178;)
Answer: F (x) = (1 + x) & # 178; (1-x & # 178;) f '(x) = 2 (1 + x) (1-x & # 178;) + (1 + x) & # 178; (- 2x) = 2 (1 + x) (1-x & # 178; - x-x & # 178;) = - 2 (x + 1) (2x & # 178; + x-1) = - 2 (x + 1) (2x-1) (x + 1) = - 2 (x + 1) & # 178; (2x-1)
f'(x)=2(1+x)(1-x^2)-2x(1+x)^2
It is reduced to: F (x) = - x ^ 4-2x ^ 3 + 2x + 1
So f '(x) = - 4x ^ 3-6x ^ 2 + 2
Given that a has 7 divisors, B has 12 divisors, and the least common multiple of a and B is 1728, then B = ()
First, write 1728 as 1728 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 (the product of the sixth power of 2 and the third power of 3)
A = 64 (about 1 24 8 16 32 64) 64 = 2 * 2 * 2 * 2 * 2
B = 108 (about 1 23 4 6 9 12 18 27 36 54 108) 108-2 * 2 * 3 * 3 * 3
Short division of 1728
1728=2*2*2*2*2*2*3*3*3
a=18 b=96