The maximum value of the function y = x + 1 x is______ ．

The maximum value of the function y = x + 1 x is______ ．

∵ function y = f (x) = x + 1 x (where x ≠ 0), ∵ f ′ (x) = 1-1 x2; Let f ′ (x) = 0, ∵ x = ± 1; then the variation of F (x) and f ′ (x) with X is as follows: ∵ when x = - 1, y = f (x) has a maximum of - 2. So the answer is: - 2

The maximum value of the function y = (x + 1) / (3 + x ^ 2) is

Find the maximum value of Y, that is, find the minimum value of 1 / y
1/y=(x-1)+4/(x+1)
=(x+1)+4/(x+1)-2
Obviously, when x > 0, y is the maximum
So we go from the mean value of 1 / Y > = 2, when x = 1
So the maximum value of Y is 1 / 2

"Function y = x + X / 1 (- 2
Using the idea of derivative to solve the problem

Let y = 0 / x + 1

cos(2π/3+2α)=2cos²（π/3+α）-1

This is the double angle formula cos2a = 2cos & # 178; A-1
Consider π / 3 + α as a (whole)
That is: cos (2 π / 3 + 2 α) = 2cos & # 178; (π / 3 + α) - 1

Why does cos2a = cos (2B + 2C) = 2cos & # 178; (B + C) + 1?

cosA=cos(-A)=cos(360-A)
Cos2a = 2cos & sup2; a + 1 are all formulas
You can also push it yourself

Cos2A=1-2Sin^A=2Cos^A-1

There is something wrong with this way of writing, but it can be understood by convention
This is the formula of double angle cosine
Cos2a = the square of 1-2 * (Sina) = the square of 2 * (COSA) - 1

Cos2a = 1-2sin & # 178; why is a equal to cos2a = - √ [1 - (sin2a) ^ 2]

Cos 2A = 1-2sin & #178; a, this is the angle doubling formula
Cos & # 178; 2A + Sin & # 178; 2A = 1, which is the transformation of the formula cos & # 178; a + Sin & # 178; a = 1
cos²2a=1-sin²2a
cos2a=-√[1-(sin2a)^2]

Reduction of 2cos square α - 4sin α cos α + 1

2cos²a-4sinacosa+1
=cos2a+1-2sin2a+1
=√5cos(2a+φ)+2
(where Tan φ = 2)

Simplification of cos2a / 2cot (π / 4 + a) cos' (π / 4-A)
The result is 1

=(cosA+sinA)(cosA-sinA)sin(π/4+A)/2cos(π/4-A)cos(π/4+A)
=[cos2A√2/2(sinA+cosA)]/[2*√2/2(cosA+sinA)*√2/2(cosA-sinA)]
=√2/2cos2A(sinA+cosA)/cos2A
=√2/2(sinA+cosA)

How can cos ^ 2 (a) be reduced to = (1 + cos2a) / 2?

cos2a=2cos²a-1
cos2a+1=2cos²
(cos2a+1)/2=cos²a