On the monotonicity of functions Given function f (x) = x / X-1, X ∈ interval [2,5] (1) The monotonicity of the function in the interval [2,5] is judged and proved (2) Find the maximum and minimum of the function in the interval [2,5]

(1) The function increases monotonically in the interval [2,5]
It is proved that in the interval [2,5], take X1 and X2, and X1 < x2
Then f (x1) - f (x2) = X1 / (x1-1) - x2 / (x2-1) = (x2-x1) / (x1-1) (x2-1)
∵x1＜x2 ∴(x2-x1)＞0
∵ X1 and X2 on [2,5]; (x1-1) > 0, (x2-1) > 0
(x2-x1) / (x1-1) (x2-1) > 0, that is, f (x1) - f (x2) > 0
∴f(x1)＞f(x2)
The function decreases monotonically in the interval [2,5]
(2) ∵ the function decreases monotonically in the interval [2,5]
∴f(x)max=2/(2-1)=2
f(x)min=5/(5-1)=5/4
Correct downstairs. I've changed it

What is the monotonicity of function in mathematics of grade one of senior high school

Compound method: it is used to find the monotonicity of compound function, that is, the derivative method of increasing with decreasing with increasing. If the derivative is greater than 0, it is increasing. Otherwise, the monotonicity of decreasing function is to study the property that when the independent variable x increases, its function y increases or decreases

If the domain of function f (x) = (MX2 + 4x + m3) - 3 / 4 + 0 (X2 - MX + 1) is r, the range of real number m is obtained

F (x) = (MX2 + 4x + m + 3) - 3 / 4 + 10 (X2 - MX + 10) 10 is defined as R MX2 + 4x + m + 3 > 0 m > 0 B ^ 2-4ac1
X2-mx + 1 ≠ 0 B ^ 2-4ac

If the function f (x) = MX / 4x-3 (x is not equal to 3 / 4) always has f (f (x)) = x in the domain of definition, then how much is m equal to

Directly write the expression of F (f (x) = x = m ^ 2x / (4mx-12x + 9) = X
When x is not equal to 0, m ^ 2-9 + (4m-12) x = 0 holds for all x in the domain
That is to say, to eliminate x is 4m-12 = 0
So m = 3

On the monotonicity of functions Given function f (x) = x / X-1, X ∈ interval [2,5] (1) The monotonicity of the function in the interval [2,5] is judged and proved (2) Find the maximum and minimum of the function in the interval [2,5]