Given f (x) = x + A / X (a > 0), find the monotone interval of F (x) 55555555555…… TT）

Given f (x) = x + A / X (a > 0), find the monotone interval of F (x) 55555555555…… TT）

Obviously f (x) is an odd function
So we only need x > 0
Let X1 > x2 > 0
f(x1)-f(x2)
=x1+a/x1-x2-a/x2
The denominator is x1x2 > 0
Molecule = X1 & sup2; x2-x1x2 & sup2; + ax2-ax1
=x1x2(x1-x2)-a(x1-x2)
=(x1-x2)(x1x2-a)
X1 > X2, so x1-x2 > 0
Then 0

If the monotone decreasing interval of function f (x) = x 2 + 2 (A-1) x + 2 is (- ∞, 4], then the real number a=

∵ monotone decreasing interval (- ∞, 4]
The axis of symmetry is 4
The formula of symmetry axis-b / 2A = 1-A = 4
∴a＝﹣3

An interval problem of mathematical function in grade one of senior high school
F (x) is an odd function on the interval (negative infinity, 0) and (0, positive infinity), and (0, positive infinity) is an increasing interval. If f (- 1) = 0, then if f (x)

According to LZ, the simplest is to draw an image
Because f (x) is an odd function on the interval (negative infinity, 0) and (0, positive infinity), and (0, positive infinity) is an increasing interval, then f (x) is a decreasing function on the interval (negative infinity, 0)
And because f (- 1) = 0, through the simple drawing lesson answer:
When f (x)

Interval problem of mathematical function in grade one of senior high school
Title: the image of the function f (x) = - x2 + 2mx-m2 + 3 is symmetric with respect to x = 2. How to find the monotone interval of the function?
I can't understand the solution of another problem
F (x) = (m-1) x2 + 2mx + 3 image on Y-axis symmetry
The axis of symmetry is x = m / (1-m) = 0, M = 0
f(x)=-x^2+3
Increasing interval: (- ∞, 0]
Minus interval: [0, + ∞)
Why do we need to solve m? With respect to Y-axis symmetry, we can see that - B / 2A = 0 directly?
Why can f (x) = - x ^ 2 + 3 get the increasing interval: (- ∞, 0) minus interval: [0, + ∞), f (x) = - x ^ 2 + 3's - B / 2a is not equal to 0?

The opening of quadratic function is downward, so it increases at (- infinity, 2) and decreases at (2, positive infinity)
If people don't ask them to find the function expression, they just need to find the monotone interval, so they don't need to calculate M