The monotone decreasing interval of the function y = cos2x is______ ．

The monotone decreasing interval of the function y = cos2x is______ ．

Because the monotone decreasing interval of function y = cosx is: [2K π, π + K π], K ∈ Z; so the monotone decreasing interval of function y = cos2x is: [K π, π 2 + K π], K ∈ Z. so the answer is: [K π, π 2 + K π], K ∈ Z

Given that the function H (x) = 4x2-kx-8 is monotone on [5,20], then the value range of K is ()
A. （-∞，40]B. [160，+∞）C. （-∞，40]∪[160，+∞）D. ∅

The axis of symmetry of the function H (x) = 4x2-kx-8 is x = K8. If the function H (x) = 4x2-kx-8 is monotone on [5, 20], then the solution of K8 ≤ 5 or K8 ≥ 20 is k ≤ 40 or K ≥ 160, so the value range of K is (- ∞, 40] ∪ [160, + ∞), so C is chosen

It is proved that the function f (x) = 2 / x + 1 is a decreasing function in the interval (- ∞, 0)
How can you help me

Let X1 < x2 < 0
f（x1）-f（x2）
=（2/x1+1）-（2/x2+1）
=2（x2-x1）/（x1x2）
And X1 < x2 < 0, so x2-x1 > 0, x1x2 > 0
So f (x1) - f (x2) > 0
That is, f (x1) > F (x2)
So f (x) = 2 / x + 1 is a decreasing function in the interval (∞, 0)

If f (x) = (| x | - 1) (x + a) is an odd function, then a=______ ．

∵ function f (x) = (| x | - 1) (x + a) is an odd function on R ∵ f (0) = - (0 + a) = 0, the solution is a = 0 test: when a = 0, f (x) = (| x | - 1) x, and f (- x) = (| - x | - 1) (- x) = - (| x | - 1) x, ∵ f (- x) = - f (x), the function f (x) is an odd function, so the answer is: 0

It is proved that f (x) = x ^ 2 + 2 / X is a decreasing function in the interval (0,1)

The derivation of F (x) shows that f '(x) = 2x-2 / x ^ 2

It is known that f (x) is an up decreasing function of R. for any x, f (KX) > F (xsquare - x + 2) can be used to find the value range of real number K

According to the definition of decreasing function, the inequality: KX less than x ^ 2-x + 2 in the range of real number is constant, that is: x ^ 2 - (K + 1) x + 2 greater than 0 in the set of real number is constant, according to the image of quadratic function, we can get the equation x ^ 2 - (K + 1) x + 2 = 0 has no real root, so the discriminant is less than 0, that is: (K + 1) ^ 2-8 is less than 0, the range of K is solved

The function x is equal to 2x square minus KX minus 8, which is a monotone function in [1,2], so we can find the value range of real number K

The solution derivation shows that f ^ and f ^ have the same sign because of monotonicity
So f ^ f ^ > is greater than 0
So k > 8 or K

Given that the function f (x) = KX ^ 3 + 3 (k-1) x ^ 2-k ^ 2 + 1 (k > 0) is a decreasing function on (0,4), find the value range of real number K

f'(x)=3kx^2+6(k-1)x
F (x) is a decreasing function in the interval (0,4), f '(x) is a decreasing function in the interval (0,4)

List the formulas
The sum of divisor, divisor, quotient and remainder is 93. The known quotient is 9 and the remainder is 2. What are the divisor and divisor?

Let the divisor be x and the divisor be y
So x + y + 9 + 2 = 93
x-2=9y
So x = 74
y=8
That is, the divisor is 74 and the divisor is 8

Make a list of the formulas
Dongdong and Lili weigh 55 kg, Dongdong and Mingming 60 kg, Lili and Mingming 65 kg. What are the weights of Dongdong, Lili and Mingming?

Weight sum of Dongdong, Lili and Mingming = (55 + 60 + 65) △ 2 = 90
Mingming's weight = 90-55 = 35 (kg)
Lili's weight = 90-60 = 30 (kg)
Weight of Dongdong = 90-65 = 25 (kg)