重难点06利用导数研究函数的零点九大题型（原卷版）_11.4-2_2026-11-04

      
      
重难点06 利用导数研究函数的零点【九大题型】

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Ï 1S2024·éêëì·íîVÞ𝑓(𝑥) = 𝑥sin𝑥+ cos𝑥−1Q𝑥∈−π
2 ,π Qï7
𝑓(𝑥)(&')
mS    V
Ay0
By1
Cy2
Dy3
žµ 1-1S2024·ðñòì·-îVÞ7
𝑓(𝑥) =
ln(1−𝑥),𝑥∈(−∞,0]
1
e|ln𝑥| ,𝑥∈(0, + ∞)
 
Qï7
𝑔(𝑥) = 𝑓(𝑥) + 𝑥+ 𝑐&'(
)
mS    V
Ay1
By2
Cy1 # 2
Dy1 # 3
žµ 1-2S2024·óô·îõö÷Vøg7
𝑓(𝑥) = 𝑎(e𝑥+ sin𝑥)−𝑥−1.
(1)Ø𝑎=
1
2¿Q3𝑓(𝑥)(¤¥†‡Ý
(2)Ø𝑎= 1¿Q𝑓(𝑥)(&')
.
žµ 1-3S2024·éêùú·îõö÷Vøg7
𝑓(𝑥) = 𝑎ln𝑥−
1
𝑥+𝑥(𝑎∈R).
(1)$%𝑓(𝑥)(&')
Ý
(2)Þå𝑥(³´µ𝑓(𝑥) ≤2𝑥−
2
eW(0, + ∞)ÃûüýQ3𝑎(¬–56.
      
      
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Ï 2S2024·éêüÁ·AîVÞ7
𝑓(𝑥) = e𝑥−𝑘𝑥2=å 0 (&'YÑþY-)Qïá
𝑘(–mS    V
Ay4
By2 e
Cy
e
2
Dye2
4
žµ 2-1S2024·ÿĀ·îõö÷Vøg7
𝑓(𝑥) = 2𝑥−𝑘𝑥−𝑏āY-)&'𝑥0QÑ𝑏> 𝑘> 0Qï𝑥0(¬–
56mS    V
Ay −∞, 1−ln2
ln2
By −∞,
ln2
1−ln2
Cy 1−ln2
ln2 , + ∞
Dy
ln2
1−ln2 , + ∞
žµ 2-2S2024·Ă㥹·AîVøg7
𝑓(𝑥) = 𝑥(e𝑥−𝑎𝑥2).
(1)ÞĆć𝑦= 𝑓(𝑥)W𝑥=−1º(Ĉć<𝑦qĉ‘Q3𝑦= 𝑓(𝑥)(¦–.
(2)Þ𝑓(𝑥)W(0, + ∞)þY-)&'Q3𝑎.
žµ 2-3S2024·ĊċČč·îõö÷Vøg7
𝑓(𝑥) = 3𝑥2 +𝑚sin𝑥(𝑥> 0)QeK𝑚ma
Ñ𝑚≥−6Q
(1)Ø𝑚= 1¿Q3Ćć𝑦= 𝑓(𝑥)W'(0,𝑓(0))º(ĈćTUQ
(2)Þ7
𝑔(𝑥) = 𝑓(𝑥)−𝑚𝑥cos𝑥W†‡ 0, 3
2 π ÃYÑþY-)&'Q3á
𝑚(¬–56.
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Ï 3S2024·éêOô·AîVÞ7
𝑓(𝑥) =
ln𝑥
𝑥−
𝑥
𝑚YŽ)&'Qïá
𝑚(¬–56mS    V
Ay(0,e)
By(e, + ∞)
Cy(0,2e)
Dy(2e, + ∞)
žµ 3-1S2024·óôĎď·îõö÷VÞ7
𝑓(𝑥) = 𝑥ln𝑥−𝑥+ |𝑥−𝑎|YÑĐYŽ)&'Qï𝑎(¬–56
      
      
JS    V
Ay −1
e ,0 ∪(0,e)
By −2
e ,0 ∪(0,e)
Cy −2
e ,0 ∪(0,3)
Dy −1
e ,0 ∪(0,3)
žµ 3-2S2024·ÿĀ·îõö÷Vøg7
𝑓(𝑥) = 𝑥e
1
𝑥−𝑎(𝑥> 0)QÑ𝑓(𝑥)YŽ)CÓ&'𝑥1,𝑥2y
(1)3á
 a (¬–56y
(2)!"
𝑥1 + 𝑥2 >
2𝑎
e y
žµ 3-3S2024·đĒôēĔĕ·îõö÷Vøg7
𝑓(𝑥) = 𝑥2ln𝑥−𝑚YŽ)³Ė(&'𝑥1，𝑥2QÑ𝑡= 𝑥2
1
+ 𝑥2
2y
(1)3á
𝑚(¬–56Ý
(2)3!
𝑡< 1Ý
(3)ėv𝑡<
2
e_2𝑚+
3
e(=>Q§!"y
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Ï 4S2024·ôċĘę·îõö÷Vøg𝑎> 1QÞ7
𝑓(𝑥) = 𝑎𝑥ln𝑎−e𝑥YŽ)³Ė(&'Qï a (¬–
56JS    V
Ay(e, + ∞)
By(1,e)
Cy(2e, + ∞)
Dy(e,2e)
žµ 4-1S2024·ĊċĚK·íîVøg7
𝑓(𝑥) = −𝑥3−3𝑥2−2𝑥,𝑥≤0
ln𝑥,𝑥> 0
 
Q𝑔(𝑥) = 𝑓(𝑥)−𝑚𝑥Y 4 )&'Q
ï m (¬–56mS    V
Ay(
1
4,
1
e)
By(−2,0] ∪{
1
e}
Cy(−2,0] ∪{
1
4}
Dy(−∞,0] ∪(
1
4,
1
e)
      
      
žµ 4-2S2024·ěďěú·-îVøg7
𝑓(𝑥) = 𝑎+ e
𝑥,𝑥> 0
e−𝑥,𝑥< 0
 
QÞTU𝑓(𝑥) + e𝑥= 0‚WA)³C´(
á/Qïá
𝑎(¬–56JS    V
Ay(−∞,e)
By(−∞,−e)
Cy(−∞,−2e)
Dy(−∞,2e)
žµ 4-3S2023·Ĝĝ=Ğ·îõö÷Vøg7
𝑓(𝑥) = 𝑥3 + 2𝑥2 + 𝑥,𝑥≥0
−2𝑥,𝑥< 0
 
QÞ7
𝑔(𝑥) = 𝑓(𝑥)−|𝑘𝑥2−4𝑥|
,(𝑘∈R)āY 4 )&'Qï k (¬–56S    V
Ay(−∞,−1) ∪2 5, + ∞
By −∞,−5 ∪(0,2)
Cy(−∞,0) ∪(0,2 + 2 2)
Dy(−∞,0) ∪2 + 2 5, + ∞
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Ï 5S2024·ôğĠď·îõö÷Vøg7
𝑓(𝑥) = ln(𝑚𝑥)−𝑥(𝑚> 0)y
(1)Þ𝑓(𝑥) ≤0ûüýQ3𝑚(¬–56Ý
(2)Þ𝑓(𝑥)YŽ)³Ė(&'𝑥1,𝑥2Q!"𝑥1 + 𝑥2 > 2y
žµ 5-1S2024·Lġ·îõö÷Vøg7
𝑓(𝑥) = 𝑎(ln𝑥+ 1) +
1
𝑥3(𝑎> 0)y
(1)3!
1 + 𝑥ln𝑥> 0Ý
(2)Þ𝑥1,𝑥2J𝑓(𝑥)(Ž)CÓ&'Q3!
|𝑥2−𝑥1| < 1−
1
𝑎y
žµ 5-2S2024·Ĝĝ·AîVøg𝑓(𝑥) = (𝑥−1)e𝑥+
1
2𝑎𝑥2.
(1)$%7
𝑓(𝑥)(¤¥}Ý
(2)Ø𝑎> 0¿Q!"
7
𝑓(𝑥)YÑĐYŽ)&'𝑥1,𝑥2QÑ𝑥1 + 𝑥2 < 0.
      
      
žµ 5-3S2024·ÿĀ·îõö÷Vøg7
𝑓(𝑥) = 𝑥2−(2 + 𝑎)𝑥+ 𝑎ln𝑥Q𝑎∈𝑅.
(1)$%𝑓(𝑥)(¤¥}Ý
(2)Õ𝑔(𝑥) = e𝑥
𝑥−𝑓(𝑥) + 𝑥2−(𝑎+ 1)𝑥−2𝑎+ (𝑎−1)ln𝑥QÞ𝑔(𝑥)‚WŽ)³Ė(&'𝑥1Q𝑥2QÑ𝑥1 < 𝑥2.
SiV!"
2𝑎> e +1Ý
SiiV!"
𝑥2−𝑥1 < 4𝑎2−2𝑎−1
2𝑎−1
.
 6  8&'(9 : ;<=>?*
Ï 6S2023·éêüÁ·AîVøg7
𝑓(𝑥) = 𝑥−
1
𝑥−𝑎ln𝑥YA)&'𝑥1,𝑥2,𝑥3QeK𝑎∈𝑅Qï𝑎𝑥1𝑥2𝑥3(
¬–56JS    
V
Ay(1, + ∞)
By 2，+ ∞
Cy(e, + ∞)
Dy(3, + ∞)
žµ 6-1S2023·éêĢģ·-îVøg7
𝑓(𝑥) = |ln𝑥−2
𝑥+ 2|−𝑚S0 < 𝑚< 3VYŽ)³Ė(&'𝑥1Q𝑥2
S𝑥1 < 𝑥2VQĤĥå𝑥1Q𝑥2(Ħzħ‰(YS    V)
①
𝑥2
𝑥1 < e2𝑚    ②𝑥1 >
2
𝑚+2    ③e
𝑚
3 < 𝑥2 <
3
3−𝑚    ④𝑥1𝑥2 > 1
Ay1
By2
Cy3
Dy4
žµ 6-2S2023·éêüÁ·-îVøg7
𝑓(𝑥) = (ln𝑥)2−
𝑎
2𝑥ln𝑥+
𝑎
e𝑥2YA)&'𝑥1 𝑥2 𝑥3Ñ𝑥1 < 𝑥2 <
𝑥3Qï
2ln𝑥1
𝑥1 +
ln𝑥2
𝑥2 +
ln𝑥3
𝑥3 (¬–56JS    V
Ay −
1
e2−e ,0
By −1
e2 ,0
Cy −1
2e ,0
Dy −2
e ,0
žµ 6-3S2023·éêĢģ·-îVøg7
𝑓(𝑥) = |ln𝑥−2
𝑥+ 2|−𝑚S0 < 𝑚< 3VYŽ)³Ė(&'𝑥1Q𝑥2
S𝑥1 < 𝑥2VQĤĥå𝑥1Q𝑥2(Ħzħ‰(YS    V)
①
𝑥2
𝑥1 < e2𝑚    ②𝑥1 >
2
𝑚+2    ③𝑥1𝑥2 > 1
      
      
Ay0
By1
Cy2
Dy3
 7  @&'*
Ï 7S2023·ĊċĨú·îõö÷Vøg𝑓(𝑥) = (𝑥−1)2e𝑥−
𝑎
3𝑥3 +𝑎𝑥(𝑥> 0)(𝑎∈𝑅).
(1)$%7
𝑓(𝑥)(¤¥}Ý
(2)Ø𝑎= 0¿Qƒ7
𝑔(𝑥) = 𝑓(𝑥) + ln𝑥−
1
2𝑥2&'()
Q§Ħ"¡.
žµ 7-1S23-24 A÷Ĝĝĩì·ĪīĬĭVøg7
𝑓(𝑥) = ln𝑥−𝑎𝑥+ 1Q𝑔(𝑥) = 𝑥(𝑒𝑥−𝑥).
S1Vޑć𝑦= 2𝑥<7
𝑓(𝑥)(€CĈQ3á
𝑎(–Ý
S2VØ𝑎= −1¿Q3!
𝑓(𝑥) ≤𝑔(𝑥) + 𝑥2.
žµ 7-2S2024·ĂăĂď·îõö÷Vøg7
𝑓(𝑥) = 𝑥e𝑎𝑥S𝑎> 0V.
(1)3𝑓(𝑥)W†‡[−1,1]Ã(•=–<•>–Ý
(2)Ø𝑎≥1¿Q3!
𝑓(𝑥) ≥ln𝑥+ 𝑥+ 1.
žµ 7-3S2023·OĮįİą·-îVøg7
𝑓(𝑥) = 𝑎e𝑥−ln(𝑥+ 1)−1y
(1)Ø𝑎= e¿Q3Ćć𝑦= 𝑓(𝑥)W'(0,𝑓(0))º(Ĉć<ŽıIJqÄ6üAB‹(ij;Ý
(2)!"
Ø𝑎> 1¿Q𝑓(𝑥)ĴY&'y
      
      
 8  AB7
(&'*
Ï 8S2023·ôċÃĵ·-îVøg7
𝑓(𝑥) = sin2𝑥+ 2sin𝑥−1Qï𝑓(𝑥)W𝑥∈[0,2023π]Ã(&')
J
S    V
Ay2023
By2024
Cy2025
Dy2026
žµ 8-1S2023·ĶĢ·îõö÷Vøg7
𝑓(𝑥) =
e𝑥+ 𝑥,𝑥< 0
sin 𝜔𝑥−π
4 ,0 ≤𝑥≤π
 
Y 4 )³Ė(&'Qïħá
𝜔
(56mS    V
Ay 9
4 , 13
4
By 9
4 , 13
4
Cy 9
4 , 13
4
Dy 9
4 , 13
4
žµ 8-2S2024·Ăċķď·AîVøg7
𝑓(𝑥) = 𝑎sin𝑥+ 𝑥cos𝑥.
(1)Þ𝑎= 0Q3Ćć𝑦= 𝑓(𝑥)W'(0,𝑓(0))º(ĈćTUÝ
(2)Þ𝑎> −1Q!"
𝑓(𝑥)W(−π,π)ÃY 3 )&'.
žµ 8-3S2024·ĂăĸĹ·îõö÷Vøg𝑓(𝑥) = 𝑥sin𝑥−𝑎cos𝑥W𝑥=
π
2¿¬¢¦=–y
(1)$%𝑓(𝑥)W[−π,π]Ã(¤¥}Ý
(2)ĺℎ(𝑥) = 𝑥2−4𝑥sin𝑥−4cos𝑥+ 4QÎℎ(𝑥)WRÃ&'()
y
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Ï 9S2024·ĂăĂď·íîVøg7
𝑓(𝑥) = 𝑎(𝑥+ 1)e−𝑥+ 𝑥2y
(1)$%𝑓(𝑥)(&')
Ý
(2)Þ𝑓(𝑥)‚WŽ)¦–'QĻ𝑥0m𝑓(𝑥)(¦=–'Q𝑥1m𝑓(𝑥)(&'Q!"
𝑥0−2𝑥1 > 2y
      
      
žµ 9-1S2024·éêļĝ·îõö÷Vøg7
𝑓(𝑥) = 𝑥−
1
𝑥+𝑎ln𝑥QeK𝑎∈𝑅.
(1)Ø𝑥∈[1, + ∞)¿Q𝑓(𝑥) ≥0Q3 a (¬–56.
(2)Þ𝑎< −2Q!"
𝑓(𝑥)YA)&'𝑥1Q𝑥2Q𝑥3S𝑥1 < 𝑥2 < 𝑥3VQÑ𝑥1Q𝑥2Q𝑥3ü´ė
ĥ.
žµ 9-2S2024·ðñĽú·íîVøg7
𝑓(𝑥) = 𝑎𝑥−ln(1−𝑥)(𝑎∈𝑅).
(1)3Ćć𝑦= 𝑓(𝑥)W'(0,𝑓(0))º(ĈćTUÝ
(2)Þ𝑓(𝑥) ≥0ûüýQ3 a (–Ý
(3)Þ𝑓(𝑥)YŽ)³Ė(&'𝑥1,𝑥2QÑ|𝑥2−𝑥1| > e−1Q3 a (¬–56.
žµ 9-3S2024·ôċľĿŀ·AîVøg7
𝑓(𝑥) = e𝑥−𝑎𝑥2Q𝑔(𝑥) = e𝑥−𝑏𝑥.
(1)Ø𝑏= e¿Q37
𝑔(𝑥)(¦–Ý
(2)øgá
𝑎∈0, e2
4 .
①3!
7
𝑓(𝑥)YÑĐY-)&'Ý
②ÕŁ&'m𝑥0QÞ𝑓(𝑥)€ÃYÑþY-ł'𝐴(𝑥1,𝑦1)Q𝐵(𝑥2,𝑦2)(𝑥1 < 𝑥2)å'(𝑥0,0)üKŃłńQ3á

𝑎(¬–56.
- ¤
      
      
1yS2024·ĊċŅņ·îõö÷V7
𝑓(𝑥) = ln𝑥+ 𝑥2−2(&'ÄW†‡JS    V
Ay 0,
2
2
By
2
2 ,1
Cy(1, 2)
Dy( 2,2)
2yS2024·ĊċċŅ·îõö÷VÞ7
𝑓(𝑥) = 𝑥3−3𝑥+ 𝑎W†‡(0,2)OYŽ)&'Qïá
𝑎(¬–56J
S    V
Ay(0,2)
By(2, + ∞)
Cy(0,1)
Dy(1, + ∞)
3yS2024·éêùú·îõö÷V7
𝑓(𝑥) = e𝑥−𝑘𝑥−𝑏āŇY-&'𝑥0QÑ𝑘> 𝑏> 0Qï𝑥0(¬–56J
S    V
Ay(−∞,0)
By(0,1)
Cy(−∞,1)
Dy(1, + ∞)
4yS2024·Ċċňê·îõö÷Vøg𝜔> 0QÞ7
𝑓(𝑥) =
ln𝑥−𝑥
3 ,𝑥> 0,
sin 𝜔𝑥+ π
3 ,−π ≤𝑥≤0
 
Y 4 )&'Qï𝜔(¬
–56JS    V
Ay 4
3 , 7
3
By 4
3 , 7
3
Cy 7
3 , 10
3
Dy 7
3 , 10
3
5yS2024·éêʼnŊ·îõö÷VƒŋW(0, + ∞)Ã(¤¥7
𝑓(𝑥)QłŌō(𝑥∈(0, + ∞)Y𝑓[𝑓(𝑥)−ln𝑥] = 1
ûüýQÞTU𝑓(𝑥) ⋅𝑓′(𝑥) = 𝑚YŽ)³Ė(á
/Qïá
𝑚(¬–56mS    V
Ay(−∞,1)
By(0,1)
Cy(0,1]
Dy(−∞,1]
6yS2024·ĶðŎŏ·îõö÷Vøg7
𝑓(𝑥) = ln𝑥+ 1−𝑎𝑥YŽ)&'𝑥1,𝑥2QÑ𝑥1 < 𝑥2QïĤĥŐħ‰
(JS    V
Ay𝑎> 1
By𝑥1 + 𝑥2 <
2
𝑎
Cy𝑥1 ⋅𝑥2 < 1
Dy𝑥2−𝑥1 >
1
𝑎−1
7yS2024·éê·îõö÷Vøg7
𝑓(𝑥) =
|3−2𝑥|+ 1,𝑥> 0,
(𝑥+2)2
e𝑥
,𝑥≤0.
 
Þ7
𝑦= [𝑓(𝑥)]2−𝑎𝑓(𝑥)Y 5 )³Ė(&'Q
ï𝑎(¬–56JS    V
Ay(0,1]
By(1,4]
Cy(1,4)
Dy(1, + ∞)
8yS2024·ÿĀ·îõö÷Vøg7
𝑓(𝑥) = e2𝑥−2(𝑎+ 1)𝑥e𝑥+𝑎(𝑎+ 2)𝑥2SeKemőÙł
(Œ
VQï
Ĥĥ%œŔ(JS    V
Ay∃𝑎∈𝑅Qŕ7
𝑓(𝑥)āY 1 )&'
By∃𝑎∈𝑅Qŕ7
𝑓(𝑥)āY 3 )&'
Cy∃𝑎∈𝑅Qŕ7
𝑓(𝑥)ĴY&'
      
      
DyÞ7
𝑓(𝑥)Y 2 )&'Qïá
𝑎(¬–56m(e−2,e)
í 8
9yS2023·Ăċ·îõö÷VøgTU𝑎𝑥−2𝑥ln𝑥= 𝑥2 +3S𝑎∈𝑅VYŽ)³Ė(/𝑥1Q𝑥2QÞ𝑥1 < 𝑥2Qï
S    V
Ay𝑎∈(4, + ∞)
By𝑥1 < 1 < 𝑥2
Cyln𝑥1 + ln𝑥2−1 > ln2
Dy𝑥1𝑥2 > 1
10yS2024·Lġ·AîVøg7
𝑓(𝑥) = 𝑒2𝑥−𝑎𝑥2(𝑎ma
)QïĤĥ%ħ‰(JS    V
AyØ𝑎= 1¿Q𝑓(𝑥)W(0,𝑓(0))º(ĈćTUm2𝑥−𝑦+ 1 = 0
ByÞ𝑓(𝑥)Y 3 )&'Qï𝑎(¬–56m(𝑒2, + ∞)
CyØ𝑎= 𝑒2¿Q𝑥= 1J𝑓(𝑥)(¦=–'
DyØ𝑎=
1
2¿Q𝑓(𝑥)Y,-&'𝑥0QÑ−1 < 𝑥0 < −
1
2
11yS2024·óôŖŗ·AîVøg7
𝑓(𝑥) = 𝑎(e𝑥+ 𝑎)−𝑥YŽ)&'𝑥1Q𝑥2QïĤĥĦzħ‰(JS    V
Ay𝑎(–Œd¬
1
4
By𝑎(–Œd¬
1
2
Cy|𝑥1−𝑥2|(–å𝑎¤¥Řř
Dy𝑓′(𝑥1) +𝑓′(𝑥2) > 0
A Śś
12yS2024·éêüÁ·AîVÞ7
𝑓(𝑥) = e𝑥−𝑘𝑥2=å0(&'YÑþY-)Qïá
𝑘(–m      
y
13yS2023·ôğ·îõö÷Vøg7
𝑓(𝑥) = 𝑥3−𝑥,𝑥≤0
ln𝑥,𝑥> 0
 
QÞ𝐹(𝑥) = 𝑓(𝑓(𝑥)−𝑡)YŜ)&'Qïá
𝑡(¬
–56J      
y
14yS2023·ŝŞŝď·íîVøg7
𝑓(𝑥) = 𝑥2e2𝑥−(𝑎+ 1)𝑥e𝑥+2𝑎−1YA)&'𝑥1,𝑥2,𝑥3QÑ𝑥1 < 𝑥2 < 0 <
𝑥3Qï(2−𝑥1e𝑥1)(2−𝑥2e𝑥2)(2−𝑥3e𝑥3)2 =      
.
é no
15yS2024·ŝŞşď·îõö÷Vøg7
𝑓(𝑥) = 𝑥3−𝑎𝑥+ 2,𝑎∈R.
(1)Þ𝑥= −2J7
𝑓(𝑥)(¦–'Q3𝑎(–Q§3e¤¥†‡Ý
(2)Þ7
𝑓(𝑥)W 1
3 ,3 ÃĐY 2 )&'Q3𝑎(¬–56y
      
      
16yS2024·éêùú·îõö÷Vøg7
𝑓(𝑥) = 2sin𝑥+ ln(𝑥+ 1)−𝑎𝑥y
(1)Ø𝑎= 2¿Q37
𝑓(𝑥)W†‡ 0, π
2 Ã&'()
Ý
(2)Þ𝑥≥0¿Q³´µ𝑓(𝑥) ≤0ûüýQ3á
𝑎(¬–56y
17yS2024·ŅŠ·AîVøg7
𝑓(𝑥) = 𝑎2𝑥−𝑥(𝑎> 0,𝑎≠1).
(1)Þ𝑎= eQ3𝑓(𝑥)W𝑥= 0º(ĈćTUÝ
(2)Þ7
𝑓(𝑥)Y 2 )&'QÎėvln𝑎<
1
2e(=>?.
18yS2024·ŝŞĢš·îõö÷Vøg7
𝑓(𝑥) =
ln(e𝑥)
𝑎𝑥QeKemőÙł
(Œ
y
(1)$%𝑓(𝑥)(¤¥}Ý
(2)ÞTU𝑓(𝑥) = 1YŽ)³Ė(/𝑥1,𝑥2y
(i)3𝑎(¬–56Ý
(ii)!"
𝑥2
1 + 𝑥2
2 > 2y
19yS2024·ĶðŢţ·íîVøg7
𝑓(𝑥) = e𝑥−𝑚𝑥,𝑔(𝑥) = 𝑥−𝑚ln𝑥y
(1)JŤ‚Wá
𝑚Qŕ¢𝑓(𝑥)9𝑔(𝑥)W(0, + ∞)Ã(¤¥†‡CĖťÞ‚WQ3r𝑚(¬–56ÝÞ³‚WQ
ŦĦ"¡y
(2)øg𝑥1,𝑥2J𝑓(𝑥)(&'Q𝑥2,𝑥3J𝑔(𝑥)(&'y
①!"
𝑚> eQ
      
      
②!"
1 < 𝑥1𝑥2𝑥3 < e3y