The maximum value of the function y = sin ^ 2x cosx is?

The maximum value of the function y = sin ^ 2x cosx is?

y=1-(cosx)^2-cosx
=-(cosx)^2-cosx+1
=-(cosx+1/2)^2+5/4
Opening down
So cosx = - 1 / 2
Y max = 5 / 4

Given the function f (x) = sin (2x + π / 6) - cos (2x + π / 3) + 2 (cosx) ^ 2 (1) find the value of F (π / 12) (2) find the maximum value of F (x) and the corresponding value of X

F (π / 12) = radical 3 + 1

Let f (x) = acos2 (square) x + bsinxcosx, and f (0) = f (π / 3) = 2
1. Finding monotone interval of function f (x)
2. Let g (x) = f (x) + KF (x + π - 6). If G (x) ≥ 3 has a solution, find the range of K

1.f(x)=a（cosx)^2+bsinxcosx,f(0)=f(π/3)=2,
∴a=2,
1/2+b√3/4=2,b=2√3,
∴f(x)=1+cos2x+√3sin2x=1+2sin(2x+π/6）,
Its increasing interval is (2k-1 / 2) π = 0, k > = 0, or K = 0, or K = 0

How to solve two equations with four unknowns,

If it is a system of homogeneous linear equations, the coefficient matrix of the system is transformed by elementary row, and infinite solutions are obtained;
If it is a system of non-homogeneous linear equations, then the augmented matrix of the system of equations is transformed by elementary row transformation. At this time, the system of equations may have no solution or infinite solutions

Xiaoxiao's father bought a coat, a hat and a pair of shoes for 140 yuan. The coat is 90 yuan more expensive than the hat. The coat and the hat are 120 yuan more expensive than the shoes. How many yuan are the coat, the hat and the shoes?

Set the hat at x yuan
X+(X+90)+(X+(X+90)-120)=140
X = 20 yuan
So hat 20 yuan, coat 110 yuan, shoes 10 yuan
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How to solve this equation?
X = R (Sina acosa), y = R (COSA + Asina), R known, x, y, a unknown, please express as the function of y = f (x), thank you

The title above says that a is unknown

3 + (5 / 3 x + 5) times 1 / 10 = 11-1 / 2x
We need to explain it in detail

3+x/6+1/2=11-x/2
Multiply both sides by six
18+x+3=66-3x
4x=45
x=45/4

Solve the equation about X: 2x / 3 + 9 = x / 2-6 (X-12)

2/3x+9=x/2-（x-12）/6
Multiply 6 on both sides to get 4x + 54 = 3x-x + 12
The result is 4x-3x + x = 12-54
Merge similar items to get 2x = - 42
If the coefficient is reduced to one, x = - 21
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Given f (x) = 3x, prove (1) f (x) · f (y) = f (x + y); (2) f (x) △ f (y) = f (X-Y)

It is proved that: (1) ∵ f (x) = 3x, ∵ f (y) = 3Y, ∵ f (x) · f (y) = 3x × 3Y = 3x + y, f (x + y) = 3x + y, ∵ f (x) · f (y) = f (x + y); (2) ∵ f (x) = 3x, ∵ f (y) = 3Y, ∵ f (x) △ f (y) = 3x △ 3Y = 3x-y, f (X-Y) = 3x-y, ∵ f (x) △ f (y) = f (X-Y)

1： It is known that f (x) = (10 ^ X-10 ^ - x) / 10 ^ x + 10 ^ - X
(1) It is proved that f (x) is an increasing function in the domain of definition
(2) Finding the range of F (x)
2： The domain of function y = f (x) is [- 2,4], then the domain of function g (x) = f (x) + F (- x) is_____ .

When you learn derivative, you can find it with derivative
Take X1 without learning derivative