The known function f (x) = x & # 178; + A / X (x ≠ 0), (constant a ∈ R) (1) If f (x) is an even function, find a (2) When the constant a ≤ 16, we prove that the function f (x) increases monotonically on [2, + ∞)

The known function f (x) = x & # 178; + A / X (x ≠ 0), (constant a ∈ R) (1) If f (x) is an even function, find a (2) When the constant a ≤ 16, we prove that the function f (x) increases monotonically on [2, + ∞)

If f (x) is even function, then f (- x) = (- x) ^ 2 + A / (- x) = f (x) = x ^ 2 + A / x2a / x = 0A = 0 (2) let 2 ≤ X1 < X2, then f (x1) - f (x2) = (x1 ^ 2 + A / x1) - (x2 ^ 2 + A / x2) = (x1 + x2) (x1-x2) + a (x2-x1) / x1x2 = (x2-x1) [A / (x1x2) - (x1 + x2] x1x2 > 4a

If the range of F (x) = LG (MX ^ 2 + 2x + 9) is less than or equal to 1, then M=

Correct answer: - 1

Given that the maximum value of the function f (x) = - x2 + mx-m / 4 + 1 / 2 in the interval [0,1] is 2, find the value range of real number M
most urgent.

F (x) is a parabola with the opening downward, and the axis of symmetry x = m / 2
When m / 2 ≤ 0, in [0,1], the function is simple minus
F (x) max = f (0) = - M / 4 + 1 / 2 = 2
The solution is m = - 6
two