F (x) = ax + 1 / a (1-x), where a is greater than 0, let g (a) be the minimum value of F (x) when 0 is less than or equal to X and less than or equal to 1 (1) Find the analytic expression of G (a); (2) find the maximum value of G (a) f(x)=ax+(1-x)/a

F (x) = ax + 1 / a (1-x), where a is greater than 0, let g (a) be the minimum value of F (x) when 0 is less than or equal to X and less than or equal to 1 (1) Find the analytic expression of G (a); (2) find the maximum value of G (a) f(x)=ax+(1-x)/a

The idea of mean inequality
（1）
Because a > 0
So f (x) = ax + 1 / a (1-x) ≥ x (1-x) under double root,
Therefore, when G (a) = double root, X (1-x) must be marked 1 > x > 0
（2）
The idea of quadratic function,
If G (a) = x (1-x) is the largest under double root sign, then G (x) = x (1-x) 1 > x > 0 is the largest
That is, when x = 1 / 2, the maximum value of G (x) is 1 / 4
When x = 1 / 2, the maximum value of G (a) is 1 / 2
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Given that the minimum value of X ≥ 2 is a and the maximum value of X ≤ - 6 is B, then a + B=______ ．

Because the minimum value of X ≥ 2 is a, a = 2; the maximum value of X ≤ - 6 is B, then B = - 6; then a + B = 2-6 = - 4, so a + B = - 4

Given that f (x) = x square-2ax-1 (0 is less than or equal to x, less than or equal to 2), find the maximum and minimum of F (x)

The value of symmetry axis-b / 2a is discussed
So the value of the axis of symmetry is x = a, if a ≤ 0, the minimum value is f (0) = - 1, and the maximum value is f (2) = 3-4A
(2) if a ≥ 2, the minimum value is f (2) = 3-4A, and the maximum value is f (0) = - 1
(3) if a = 1, the maximum value is f (0) = f (2) = - 1, and the minimum value is f (1) = - 2
(4) if 0

Let f (x) = x squared - 2aX (o ≤ x ≤ 1) be m (a) and n (a) the maximum and minimum values of F (x) = x squared - 2aX (o ≤ x ≤ 1)

F (x) = x ^ 2-2ax = (x-a) ^ 2-A ^ 2 x belongs to [0,1]
When a belongs to (- ∞, 0]
M（a）=1-2a.x=1 N（a）=0.x=0
When a belongs to [1, + ∞)
M（a）=0.x=0 N(a)=1-2a.x=1
When a belongs to (0,1 / 2)
N（a）=-a^2.x=a M(a)=1-2a.x=1
When a belongs to [1 / 2,1]
N（a）=-a^2.x=a M（a）=0.x=0