已知定义在R上的函数F（x）满足F（x+y）=F（x）+F（y），当x＞0时，F（x）＜0，且对任意的x∈[0，1]，不等式组
（1）求证：函数F（x）在R上为减函数 （2）求实数k的取值范围． |
（1）设x1＜x2，则x2-x1＞0∴F（x2-x1）＜0 …（1分）
∴F（x2）=F（x2-x1）+F（x1）＜F（x1）∴函数F（x）在R上为减函数 …（4分）
（2）∵函数F（x）在R上为减函数∴
对x∈[0，1]成立，…（6分）2kx-x2＞k-4 x2-kx＞k-3
依题有
对x∈[0，1]成立f(x)=x2-2kx+k-4＜0 g(x)=x2-kx-k+3＞0
由于f（x）＜0对x∈[0，1]成立∴
∴-3＜k＜4①…（10分）f(0)＜0 f(1)＜0
由于g（x）＞0对x∈[0，1]成立∴k＜
=x2+3 x+1 (x+1)2-2(x+1)+4 x+1
∴k＜(x+1)+
-2恒成立∴k＜2②…（14分）4 x+1
综上由①、②得-3＜k＜2…（16分）
请认真阅读下面短文，并根据所读内容在文章后图表中的空格里填入最恰当的单词。注意：每空不超过1个单词。 Whenever we meet with difficulty or failure, teachers, parents or others often say to us or perhaps we say to ourselves, “Never give up.” These can be encouraging words and words of determination. A person who believes in himself will keep trying to reach his goal no matter how many times he fails. In my opinion, the quality of determination to succeed is an important one to have. Therefore, I believe that we should never give up. One reason is that if we give up too easily, we will rarely achieve anything. It is not unusual for us to fail in our first attempt at something new, so we should not feel disappointed and should try again. Besides, if we always give up when we fail, we will not be able to develop new skills and grow. Another reason we should never give up is that we can learn from our mistakes so that we can not make the same ones. If we do not try again, the lesson we have learned is wasted. Finally, we should never give up because as we work to reach our goals, we develop confidence, and this confidence can help us succeed in other areas of our lives. If we never challenge ourselves, we will begin to doubt our abilities. In short, it is important that we do not give up when working for our goals. Whether we succeed in the end or not, we will learn something, and what we learn will help us to become better and more confident. Furthermore, if we give up, we have no chance of attaining our goals any more , but if we keep making great efforts, there is always a chance that we will succeed one day. Topic: Never Give Up
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