If the function y = 3x2 - (9 + a) x + 6 + 2A (x is an independent variable and X is an integer) gets the minimum value when x = 6 or x = 7, then the value range of a is______ ．

If the function y = 3x2 - (9 + a) x + 6 + 2A (x is an independent variable and X is an integer) gets the minimum value when x = 6 or x = 7, then the value range of a is______ ．

The axis of symmetry of parabola is a straight line x = - - - - - (9 + a) 2 × 3 = 9 + A6, ∵ when x = 6 or x = 7, the minimum value is obtained, X is an integer, ∵ 9 + A6 > 5.5 ① 9 + A6 < 7.5 ②, solving inequality ①, a > 24, solving inequality ②, a < 36, so the solution of inequality group is 24 < a < 36, that is, the value range of a is 24 < a < 36

If the minimum value of function f (x) = 2 | x + 7 | - | 3x-4 | is 2, find the value range of independent variable x

According to the meaning of the title, when x ＞ 43, the inequality is x + 7 - (3x-4) ≥ 1, and the solution is x ≤ 5, that is 43 ＜ x ≤ 5 (3 points); when − 7 ≤ x ≤ 43, the inequality is x + 7 + (3x-4) ≥ 1, and the solution is x ≥ 12, that is − 12 ≤ x ≤ 43. & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (4) when x < 7-7, when x < 7-7, the inequality is-x-7 + (3x-4) ≥ 1, and the solution is & nbsp; X ≥ 6, and the contradiction with x < 7, which is the case of x-7-7, when x < 7-7, the inequality is-x-7-7-7-7-7-7-7, and the solution is & nbsp; X ≥ 6, and the contradiction between X and x < 7-7-7, which is the solution & nbsp; 6, and the contradiction of X-6, and the contradiction of x-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-6-6-6, and the& nbsp; & nbsp; &Nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (7 points)

Given the function y = 6-3x. Draw the function image and value range

This is a linear function, so its image is a straight line. The intersection of this line with X axis is a (2,0), and the intersection with y point is B (0,6). Drawing a line AB connecting a and B is the image of this function. The value range is: X belongs to R, y belongs to R

x. Y belongs to R and f (x) + F (y) = f (x + y) is constant when x > 0, f (x)

Let x1

The monotonicity of function f (x) = x2-2ax + 3 in (- 2,2) is discussed

The axis of symmetry equation of the function f (x) = x2-2ax + 3 is: x = a, when a ≤ - 2, the function f (x) = x2-2ax + 3 monotonically increases in the interval (- 2, 2); when - 2 < a < 2, the function f (x) = x2-2ax + 3 monotonically decreases in the interval (- 2, a) and monotonically increases in the interval [a, 2]; when a ≥ 2, the function f (x) = x2-2ax + 3 monotonically decreases in the interval (- 2, 2)

The monotonicity of function f (x) = x2-2ax + 3 in (- 2,2) is discussed

The equation of axis of symmetry of function f (x) = x2-2ax + 3 is: x = a, when a ≤ - 2, the function f (x) = x2-2ax + 3 monotonically increases in the interval (- 2, 2); when - 2 < a < 2, the function f (x) = x2-2ax + 3 monotonically decreases in the interval (- 2, a) and monotonically increases in the interval [a, 2]; when a ≥ 2, the function f (x)

The monotonicity of function f (x) = x2-2ax + 3 in (- 2,2) is discussed

The equation of axis of symmetry of function f (x) = x2-2ax + 3 is: x = a, when a ≤ - 2, the function f (x) = x2-2ax + 3 monotonically increases in the interval (- 2, 2); when - 2 < a < 2, the function f (x) = x2-2ax + 3 monotonically decreases in the interval (- 2, a) and monotonically increases in the interval [a, 2]; when a ≥ 2, the function f (x)

Given f (x) = x / X & # 178; + 1 x ∈ (0, + ∞), the monotonicity of function f (x) can be obtained

f（x）=x/(x²+1)
f'(x)=(x²+1-2x²)/(x²+1)²
=-(x+1)(x-1)/(x²+1)²
From F '(x) > 0 to (x + 1) (x-1)

The monotonicity of function y = (AX) / (AX & # 178; - 1), X ∈ (- 1,1), a ≠ 0 is discussed and proved

If you deal with the right side of the function expression and change the numerator to 1, you can easily see that the denominator is monotonous

Let 1 / 3x3 + ax, G (x) = - X & # 178; - A (∈ R)
(1) If the function f (x) = f (x) - G (x) increases monotonically in the interval [1, + ∞), the minimum value of a is obtained

The minimum value of a = - 1
F (x) = f (x) - G (x) = 1 / 3x ^ 3 + ax + A ^ 2 + A
F '(x) = x ^ 2 deca
F (x) = f (x) - G (x) increases monotonically on the interval [1, positive infinity]
x>=1
F '(x) = x ^ 2 + a > = 0
1 ten a > = 0
a>=-1
The minimum value of a = - 1