(1) y=x+(2^b)/x(x>0)值域为6时,2^b=9,所以 b=log(2) 9
(2)y=x^2+c/(x^2)(c>0)有y=u+c/u, u=x^2复合而成,u=x^2在[0,4√c ],[4√c,+∞]递增,对应y=u+c/u在(0,√c]递减,在[√c,+∞)递增,
所以(0,+∞)内(0,4√c ]为递减,[4√c,+∞]为递增
y=x^2+c/(x^2)为偶函数,[-4√c,0 )为递增,[-∞,-4√c ]为递减
所以 递增区间为[-4√c,0 ),[4√c,+∞] 递减区间为[-∞,-4√c ],(0,4√c ]
(3)推广函数: y=x^n+a/(x^n)(a>0)
n为偶数时 y=x^n+a/(x^n)(a>0)为偶函数
递增区间为[-2n√a,0 ),[2n√a,+∞] , 递减区间为[-∞,-2n√a ],(0,2n√a ]
n为奇数时 y=x^n+a/(x^n)(a>0)为奇函数
递增区间为[-∞,-2n√a ],[2n√a,+∞] , 递减区间为[-2n√a,0 ),(0,2n√a ]
(2n√a 表示2n次根号下a,其他类似)
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