The maximum value of function f (x) = √ X / (x + 1) is. Please use mean inequality to solve the problem

The maximum value of function f (x) = √ X / (x + 1) is. Please use mean inequality to solve the problem

F (x) = √ X / (x + 1) numerator denominator divided by √ x
=1/(√x+1/√x)
≤ 1 / {2 √ [(√ x) (1 / √ x)]} (the smaller the denominator, the larger the score)
=1/2
So the maximum value of function f (x) is 1 / 2

Given the function y = x + 16x + 2, X ∈ (− 2, + ∞), then the minimum value of this function is______ ．

∵ x ∈ (- 2, + ∞), ∵ x + 2 & gt; 0, from the basic inequality, y = x + 16x + 2 = x + 2 + 16x + 2-2 ≥ 2 (x + 2) × 16x + 2-2 = 6, if and only if x + 2 = 16x + 2, that is, x + 2 = 4, take the equal sign "=" when x = 2, then the minimum value of this function is 6

Given the function y = x + 16x + 2, X ∈ (− 2, + ∞), then the minimum value of this function is______ ．

∵ x ∈ (- 2, + ∞), ∵ x + 2 & gt; 0, from the basic inequality, y = x + 16x + 2 = x + 2 + 16x + 2-2 ≥ 2 (x + 2) × 16x + 2-2 = 6, if and only if x + 2 = 16x + 2, that is, x + 2 = 4, take the equal sign "=" when x = 2, then the minimum value of this function is 6