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问题 解答题

已知函数f（x）=3ax-2x2+lnx，a为常数．

（1）当a=1时，求f（x）的单调区间；

（2）若函数f（x）在区间[1，2]上为单调函数，求a的取值范围．

答案

（1）当a=1时，f（x）=3x-2x2+lnx，则f（x）的定义域是（0，+∞）

∵f′(x)=3-4x+

1
x
=
-4x2+3x+1
x
=
-(4x+1)(x-1)
x
．

∴由f′（x）＞0，得0＜x＜1；由f′（x）＜0，得x＞1；

∴f（x）在（0，1）上是增函数，在（1，+∞）上是减函数．

（2）∵f′(x)=3a-4x+

1
x
．

若函数f（x）在区间[1，2]上为单调函数，

则f′（x）≥0，或f′（x）≤0在区间[1，2]上恒成立．

∴3a-4x+

1
x
≥0，或3a-4x+
1
x
≤0在区间[1，2]上恒成立．

即3a≥4x-

1
x
，或3a≤4x-
1
x
在区间[1，2]上恒成立．

设h（x）=4x-

1
x
，

∵h′（x）=4+

1
x2
＞0

∴h（x）=4x-

1
x
在区间[1，2]上是增函数．

h（x）max=h（2）=

15
2
，h（x）min=h（1）=3

∴只需3a≥

15
2
，或3a≤3．

∴a≥

5
2
，或a≤1．

单项选择题

再生障碍性贫血

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                                                      How to Make a Budget (预算)
     Most likely, you aren't the family breadwinner. But doing a small job or getting a weekly allowance (零花钱)
would put some money in your pocket. For kids and grown-ups alike, money is easy to spend. If you aren't
careful, it can be gone in no time. Being responsible with your money is an important skill to learn－and the
sooner you start the better. Whether you are tracking your spending or saving for something special, creating
a budget can help you deal with your expenses and plan for the future. All you need are paper and a pencil－and
some self-control. First, take a look at our sample monthly budget. Then, use a separate sheet of paper to plan
your own. In the first two columns (栏), list your sources (来源) of income and how much you expect to earn
form them. In the third and fourth columns, list what you expect to spend your money on and the amount.
    The left-hand total should
be more than or equal to the
right-hand total. If it is, you
have an effective budget.
     Budgets are not complex,
but sticking to them can be
tough. When planning your
budget, be realistic about
your expenses. If you know		                                       Sample Monthly Budget
Monthly IncomeAmount    Monthly Expenses Amount
Allowance$ 20.00Snacks $ 26.00
Money earned
Selling drinks		$ 25.00Music downloads$ 12.00
Money earned
babysitting		$ 12.50Movies$ 18.00
Money earned $ 30.00 Video rentals $ 10.00
that you drop $ 18 at a movie, don't write $ 12 in that space simply because you wish you were spending less.
     If you are eyeing a big purchase, such as a $ 150 skateboard, spend less and save more until you have the
total amount. No matter how attractive it may be, avoid spending your savings. One day, you will thank yourself?
1. Who is the passage written for?
A. Children
B. Parents.
C. Breadwinners.
D. Bank managers.
2. The purpose of making a budget is to help people ______.
A. learn to be realistic
B. increase their savings
C. manage their money well
D. test their power of self-control
3. What should people do when planning a budget?
A. Fill in the expenses as they really are.
B. Avoid spending money on expensive things.
C. Set aside a fixed amount of money as savings.
D. List income and expenses on two pieces of paper.
4. Which of the following budgets is effective?
A.
B.
C.
D.
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