> 数学 >
设x,y都大于零,求【x+y][1/x+25/y]的值
人气:367 ℃ 时间:2020-10-01 23:23:19
解答
设x,y都大于零,求【x+y][1/x+25/y]的值?
f(x,y) = (x + y)(1/x + 25/y) = 1 + 25x/y + y/x + 25 = 25x/y + y/x + 26
令x/y = u
g(u) = 25u +1/u +26
g'(u) = 25 - 1/u^2 = 0
u = 1/5
g''(u) = 2/u^3 > 0
g(1/5) = 36 为最小值.
f(x,y)的值域为(36,+∞)
推荐
猜你喜欢
© 2024 79432.Com All Rights Reserved.
电脑版|手机版