If lgx + lgY = 1, then the minimum value of 1x + 1y is______ ．

If lgx + lgY = 1, then the minimum value of 1x + 1y is______ ．

From lgx + lgY = lgxy = 1, we get xy = 10, and X ＞ 0, y ＞ 0, 〈 1x + 1y = x + YXY ≥ 2xyxy = 21010. If and only if x = y, we take the equal sign, then the minimum value of 1x + 1y is 21010. So the answer is: 21010

The minimum value of F (x) = 4x & # 178; - x

f=(2x-0.25)^2-1/16
X = 1 / 8 is the minimum, and the minimum is - 1 / 16

Let f (x) be defined on (0, + ∞), f (1) = 0, f '(x) = 1 x, G (x) = f (x) + F' (x). Find the monotone interval and minimum value of G (x)

Let f (x) = LNX, G (x) = LNX + LX, G '(x) = x-1x2, let g' (x) = 0, and get x = 1. When & nbsp; X ∈ (0,1), G '(x) < 0, so (0,1) is the monotone decreasing interval of G (x); when x ∈ (1, + ∞), G' (x) > 0, so (1, + ∞) is the monotone increasing interval of G (x), so x = 1 is & nbsp; Therefore, the minimum value is g (1) = 1