Given that the maximum value of function f (x) = AXF / x ^ 2 + A is 1 / 2, find the value of real number a It is known that the maximum value of F (x) = ax / x ^ 2 + A is 1 / 2 How to find the value of real number a Second, if f (x) is a decreasing function in the interval (m, 2m-1), find the value range of real number M Finding the maximum and minimum of derivative f '(x) of function f (x)

Given that the maximum value of function f (x) = AXF / x ^ 2 + A is 1 / 2, find the value of real number a It is known that the maximum value of F (x) = ax / x ^ 2 + A is 1 / 2 How to find the value of real number a Second, if f (x) is a decreasing function in the interval (m, 2m-1), find the value range of real number M Finding the maximum and minimum of derivative f '(x) of function f (x)

If f '(x) = [a (x ^ 2 + a) - ax (2x)] / [(x ^ 2 + a) ^ 2] = - A (x ^ 2-A) / (x ^ 2 + a) ^ 2 (1) Let f' (x) = 0, then x = ± √ a, when a ＞ 0; (Note: if a ＜ 0, f (x) increases continuously, there is no minimum value, so it should take a ＞ 0) when x ＜ - √ a, f '(x) ＜ 0, f (x) decreases; when - √ a ＜ x ＜ a, f'