The function y = 3sin (2x + π) 6) Monotone decreasing interval () A. [kπ−π 12，kπ+5π 12]（k∈Z） B. [kπ+5π 12，kπ+11π 12]（k∈Z） C. [kπ−π 3，kπ+π 6]（k∈Z） D. [kπ+π 6，kπ+2π 3]（k∈Z）

The function y = 3sin (2x + π) 6) Monotone decreasing interval () A. [kπ−π 12，kπ+5π 12]（k∈Z） B. [kπ+5π 12，kπ+11π 12]（k∈Z） C. [kπ−π 3，kπ+π 6]（k∈Z） D. [kπ+π 6，kπ+2π 3]（k∈Z）

By using the monotone decreasing interval of y = SiNx, π can be obtained
2+2kπ≤2x+π
6≤3π
2+2kπ
∴kπ+π
6≤x≤kπ+2π
Three
The function y = 3sin (2x + π)
6) Monotone decreasing interval [K π + π
6，kπ+2π
3]（k∈Z）
Therefore, D

In the same rectangular coordinate system, draw the following functions: (1) y = - 4 / X; (2) y = 2-3x (3) y = - 3 / X

(1) Y = - X / 4 positive proportional function, straight line passing through the origin - two points can be used to (0,0), (4, - 1) (2) y = 2-3x linear function, straight line, x = 0, y = 2, passing (0,2) point y = - 1, X = 1, passing through (1, - 1) (3) y = - 3 / X - inverse scale function

Function y = 1 The number of intersection points of X and y = x images in the same plane rectangular coordinate system is () A. 1 B. 2 C. Three D. 0

Function y = 1
In X, when k > 0, it passes through one or three quadrants;
The image of y = x crosses the first and third quadrants
So there are two intersections
Therefore, B

The image of the function y = ax power and y = - logax (a > 0 and a ≠ 1) in the same coordinate system is

The image of these two functions has a great relationship with the value of A. when a = 1 / 2, y = (1 / 2) ^ x is a decreasing function, y = - loga (x) = - log2 (x) / log2 (1 / 2) = log2 (x), is an increasing function: when a = 2, y = 2 ^ x is an increasing function, y = - loga (x) = - log2 (x) / log2 (2) = - log2 (x), is

In the same coordinate system, draw the image of function y = x, y = - 2x, y = 1 / 2x, y = 3x

The image of the function y = x, y = - 2x, y = 1 / 2x, y = 3x in the same rectangular coordinate system is shown in the following figure:

Let f (x) = 3sin (Wx + π / 6), w > 0, X belong to R, and take π / 2 as the minimum positive period (1) to find the analytic formula of F (0)? (2)? (3) Given that f (A / 4 + π / 12) = 9 / 5, find the value of sina A is α

According to the formula t = 2 π / w  w = 4  f (x) = 3sin (W0 + π / 6), = 3sin (π / 6) = 3 / 2, π / 2 is the minimum positive period  according to the formula t = 2 π / w  w = 4  f (x) = 3sin (4x + π / 6) the third question f (A / 4 + π / 12) = 9 / 5 9 F (A / 4 + π / 12) = 3sin (4 (A / 4 + π / 12) + π / 6) = 3sin (a + π / 3 + π / 6) = 3sin (a + π / 3 + π / 6) = 3sin (a + π / 3 3 cos (a) = 9 / 5, so cosa = 3 / 5

Find the derivative of function y = cos (4-3x)

y'=-sin(4-3X)*(-3)=3sin(4-3X)

The period of function y = 1 / 2Sin (3x + 2 π / 5) Minimum period

Period generally refers to the minimum period
The period of SiNx is 2K π (K ∈ n +)
So let 3x = 2K π
x=2kπ/3
kmin=1
So the period of the function is 2 π / 3

Finding the monotone interval of function y = sin (cosx)

0

0

∵ function f (x) = (a + 1)
Ex − 1) cosx is an odd function,
∴f(−x)＝(a+1
e−x−1)cos(−x)=−f(x)＝−(a+1
ex−1)cosx
That is, a + 1
e−x−1＝a+ex
1−ex=−(a+1
ex−1)
The solution is a = 1
2．
Therefore, D