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问题 填空题

若关于x的不等式x2+1≥kx在[1，2]上恒成立，则实数k的取值范围是______．

答案

∵关于x的不等式x2+1≥kx在[1，2]上恒成立，

∴k≤x+

1
x
，

∵x+

1
x
在[1，2]上的最小值是当x=2时的函数值2，

∴k≤2，

∴k的取值范围是（-∞，2]

故答案为：（-∞，2]．

解答题
计算：
（1）-8
3
+
2
3
2
(保留三个有效数字，
3
≈1.732，
2
≈1.414)；
（2）2
3
+
5
2
-10
0.04
（精确到0.01，
3
≈1.732，
5
≈2.236）．
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问答题

Andy was the managing director of Alpha Pte Ltd (‘Alpha’), a computer technology company. Andy was tasked by Alpha to actively pursue and negotiate a contract with Beta Pte Ltd (‘Beta’) to develop a revolutionary internal audit software. However, Beta was not keen to enter into the joint venture with Alpha and preferred to work with Andy instead. Andy resigned from his post with Alpha and personally entered into the contract with Beta. When the internal audit software was developed and became a huge commercial success, Andy made a large profit.Required:Discuss whether Andy has breached any duty as a director of Alpha when he entered into the contract with Beta, and the consequences of such a breach. (10 marks)
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