Find the maximum value of the function y = 2x + (1 / x) (x is less than 0)

Find the maximum value of the function y = 2x + (1 / x) (x is less than 0)

∵x0,1/(-x)>0
y=2x+(1/x)
=-[-2x+1/(-x)]
≤-2√[-2x·1/(-x)]
=-2√2
When - 2x = 1 / (- x), i.e. x = - 2 / 2, the maximum value is - 2 √ 2

Let a > 0 be a constant and find the maximum and minimum values of the function y = e ^ (- x) - e ^ (- 2x) in the interval [0,1]
Wrong interval. Yes, [0, a] let's calculate again,

f′(x)=-e^(-x)+2e^(-2x),
F (x) ′ = 0, the stationary point x = LN2 belongs to [0,1]
0

Given that the function f (x) = ax + 1 x + 2 is an increasing function in the interval (- 2, + ∞), then the value range of real number a ()
A. a＞12B. a≤−12C. a≤12D. a≥-12

F ′ (x) = a (x + 2) − (AX + 1) (x + 2) 2 = 2A − 1 (x + 2) 2, because f (x) is an increasing function on (- 2, + ∞), so f ′ (x) ≥ 0 is constant, that is, 2a-1 ≥ 0, the solution is a ≥ 12, and when a = 12, f (x) = 12 is not monotone, so the value range of real number a is a > 12, so select a

The monotone increasing interval of the function y = (13) x2 − 2x is______ ．

∵ function y = (13) x2 − 2x = 3 − x2 + 2x, according to the monotonicity of composite function, this problem is to find the increasing interval of function T = - x2 + 2x = - (x-1) 2 + 1. By using the properties of quadratic function, we can get that the increasing interval of function T = - (x-1) 2 + 1 is (- ∞, 1), so the answer is: (- ∞, 1]

The monotone increasing interval of function f (x) = x ^ 2-2x-3 is

x ²-2x-3
=(x-1)²-4
x

What is the symmetry of the image of the function f (x) = x minus x

On origin symmetry

Given that the image of function f (x) and the image of function H (x) = x + 1 / x + 2 are symmetric with respect to point a (0,1), the analytic expression of F (x) is obtained

Suppose B (a, b) is in H (x)
b=a+1/a+2
Let C and B be symmetric with respect to a, then the midpoint of BC is a
So C (- A, 2-B)
He is in F (x)
That is, f (- a) = 2-b
That is, x = - A, y = 2-b
a=-x,b=2-y
So 2-y = - X-1 / x + 2
y=x+1/x
So f (x) = x + 1 / X

A, y = 1 / 4 (x-23) + 155 B,. Y = 1 / 4 (x + 23) square + 155 C,
Y =. Y = quarter (x + 23) square + 155
d. Y =. Y = quarter (x + 23) square + 155

If it is followed by + 155, then
Y = - 1 / 4 (x + 23) & # 178; + 155 or y = - 1 / 4 (x-23) & # 178; + 155
(the typing of the original question is wrong, but the correct answer is not found. The above functions are for reference.)

Write out a linear function whose coordinates of intersection of image and X axis are (3,0)

Let y = ax + B. let x = 3, y = 0 be taken in, and 3a = - B. so y = x-3, y = 2x-6, y = 3x-9 Y = nx-3n

If the image of a function y = 2x + B passes through a point (0,1), then the coordinates of the intersection of the image and the x-axis are
Plus points for answers within 5 minutes

The coordinate of the intersection point (- 1 / 2,0) between the image and the x-axis of the linear function y = 2x + B passing through the point (0,1) y = 2x + 1