已知函数y=x+
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(x>0)有如下性质:如果常数a>0,那么该函数在(0,
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]上是减函数,在[
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,+∞)上是增函数.
(1)如果函数y=x+
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(x>0)的值域为[6,+∞),求b的值;
(2)研究函数y=x
2+
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(x>0,常数c>0)在定义域内的单调性,并用定义证明(若有多个单调区间,请选择一个证明);
(3)对函数y=x+
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和y=x
2+
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(x>0,常数a>0)作出推广,使它们都是你所推广的函数的特例.研究推广后的函数的单调性(只须写出结论,不必证明),并求函数F(x)=
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+
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在区间[
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,2]上的最大值和最小值(可利用你的研究结论).
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