构造函数(导数单调性)

222222构函数导数调）一选择

()()[]()A())()B())()C())D()()()

()R)))<

(1)

()<

()A{

1}B{>1}C{1D{1<<1}()(∞)()A()()B()()C()()D)()

)()<

R()

2

()AB(2013)eC(2

22(0)222(0)22D

()R(1)1)>1

(()AB1,0)(0,1)C∞)D(∪(1∞)

)(∈(1))()>0

)A(1)(0,1)B1,0)(1∞)C∪(1,0)D(0,1)(1∞)

()(∈)′()>()()AB≤e

(0)(0)C(2)eD

(0)

R()(1))′()R)<1(∈)(1()A∞)B1)CD(∪(1∞)

)R(∈R

(

()

22222222A(1,1)B1

∞)C1)D(∞)10.

(()R<0

′()()()′((0

f())<0

()A(3,0)∞)B3,0)(0,3)C∪∞)D(∪(0,3)(()

R())<()∈A

(0)(2016)>e

(0)B(2)<e

2

(0)C(2)<eD

2(0)(0)(2016)<e(0)12.

(R(017∈R成f2013

()A(2,2)B2

∞)C2)D(∞)13.

()()

)()))<0

<()

A()()()B()()>()C()()()D)()()14.

R()′()f()(0)2(x()A(0)B2)C∞)D(2∞)15.

)R∈()<(()()

)a

()b(1)(log)(log)

a()A>>B>aC>D>16.

()R1)1

(()>()A(1,0)B∞)C1,0)∪∞)D(∪(1∞)17.

))≠0

)

>0(1)

((ln)(ln)A<<B<C<D<b

)18.

()()f()·tanx恒()A

()<()B

()>

()C

()>()D(1)<2()·sin119.

()R>0

f)>0()A(1,0)∞)B1,0)(0,1)C∪∞)D(∪(0,1)20.

R()<()(2)(4)1

()<e()A(∞)B∞)C∞)D(4∞)21.

(R(013∈R成f2

009

()A(2,2)B2

∞)C2)D(∞)22.()()R())(()()

A2BC9D

()23.

(∞)()(

>

()ABCD(2)<224.

R()≠0

)

(22)ln2(ln()A>>cB>CaD>

25.

)()R①()

(②()③()·′()>′()·()ABC2D2

()26.

()R

x)<32

()A(0)B∞)CD(1∞)二、填空题27.

)R(1)0

_______28.

()

()

(

)

∈(

()

′(

a

)

b(ln(ln2)(log)·(log)________29.()(∞)′()≥()()(()(≤)30.

)(1∈()>34

________

31.

R()(1)1∈R

(lg)>

________32.

()(0)′()3())>0((015)(3)>0

_______33.

f()(∈R′())>())>(0)e________34.

)

(

0)(0

π)

)

0<<

)cossin()>0(<0

________35.

)∈)()sin>0

________①

()<(②

()<

()③(0)<

()④()<

()三、解答题

答案解析f)<′()′(′()<0)()()[]

()()

())()()

())()

()

)<

∴()<

(()∴()<(1)∵))<0∴()∴

A()(∈∞)))()∴()∈(0∞)()∵∴()())()

()())e()()())∵∴)>0

∴()R∴(2(2

∴e2015)>e2(2013)∴(2(2013)e

()()(1)′(

(1)0

′())R(1)0.()>

()>0

(1∞)A))

)

′(

()

(0

()(∈R

()

((1)0.

<1

()>0(1

()<0()>0()>0

(∞1)∪D())∴()R(2)>

∴

>

Af(

))()))1<0(1)(1)11()<(1)>1.

()()4)

22))2>0(R(1)(2>()>24.10.

D()()()∵))()()∴()<0

∵)()())·())∴(0∞)(3)0(3)0.

()()<0∈∞∪(0,3)C

)

)

∴)

R∴(2)<(0)

<

(2)<e

(2016)<e

12.

()()013)′()<0∴()R(2)(4

0130172

∴<((0∴(2

(2)13.

[

]′()()()′(

R<

>>

((()())14.

()

)∵()>)

∴

()∵(0)

∴(0)(0)

(∵()∴>0(∞)

15.

A

)R∴∈∞0)′()<()()()))(∴∈∞0)(()∴∈(0∞)

(

()()(1)(1)(log)(log)(log)2)(2)∵<2∴(1)<(<

)<(2)16.

()R(∴()

∴)

∴()(∞)(0)1

∴(1)

∵)>∴

>1((1)∴∵

∴

<1((∴

(0)0f()>

f()>x17.D

(1,0)∪∞)

()(′()()′()[)

]∵

′()

∴>0

)>0

∴()(∞)

∵()∴22(2)(ln)(ln)(ln(ln2)(ln2)(ln2)(1)1(1)∵ln2<1<2()(0∞)∴(ln(2)(ln2)(ln(1)<2(2)∴<<.

18.

A∈(0)sincos>0)<)tan(<)sin()cos()

∈(0)

)∈(0))<()<()

<<.2()<

()<<()

()<(

()<

()()<()(1)>2(ABD19.D]′<0[

(∞)(1)(0,1)((∞)

(()R(1)()>0

(∞∪20.

(2)∴2)0

∴()2∴(4)

∵(4)1∴

(

(∈R)

22)∵)<()∴)(∴∴(∵()<e∴()<1∵(0)∴()<(0)∴21.()()2

2009))

∴()(∴(((

20.∴(2009)>∴<

(

(2)22.

D()()∴

∵)(()′()∴[

]

ax<1.)()

∴

()23.

()()()′()((∞)∈∞)

′()<0

>x

∈(0∞))<0)(∞)(3)>3

24.

D()()()′()∵≠0

′()

∴

)()>0

()∵)∴2((2)2(ln∵2>ln

∴(2)>(ln()>>25.

①

∴[

]②()③()·′()>()()()·′([

]

R

22∵2.26.

D()()3∵′(∴))3<0∴()R∵(1)∴(1)(1)5

2.∵()<32

∴()3

∴()<(1)∵()R∴(∪(1∞)

[

]

>0(

<

()<0.)1<

()(1

()(()>0

(1,0)∪(1∞)<<)())R()R∈)())<0

∴)((0∞)∵3>22<1|log

>ln(2

)<

(2

)(ln2)(log(log)∴<<.≤())[()]∵′()()

∴))(0∞)

≥>0

)(∴

≤

)()(1

∞)()()(3(1)((4)1

∈R)>3∴))∴()R∴()>0

(∞)

)>3(∞)(0,10))<

∴)

∴()

R)(

)R∵(1)

∴(1)(1)1

1

0(lg)

(lg(1)∵()R∴

∴<10∴0,10)(2018015))3()3(′()

[3()′()]

∵∈∞0)()∴

∴((0)(227((015)(2015)>(3((015)>3)∴015>32∴(20182015)(0∞)()∵∈∴)

∴()R(

>(0)∵()