CC BY
7UUBbUUShîUîUû SÜSbUUQhSni-BúnKU
<U3Î ßUUUL3Ub
<äS<pшpâpшqnLJÚ úшßbúшлf^L|ШJf^ шúpf^núf^ шuf^uлbúл, фf^qf^L|шúшßbúшлf^L|шL|шú qf^лnLßJnLÚúbpf^ ßb|úшónL
SbSbUUQhSUMUb Pbn-3©h ПРПС ÊmhPbbPh Ln-DUUb UbßnObbP UbM önönbUMUbh $nKU48hU3h UÖUbS3ULh MhPUPn^UUP' «PUP9PUQn-3b UUObUUShMU» ^UUÜbBUSh CPaUbUMnhU
U2ËшлшúùD ÚL[f^pL[шó t úbii фnфnflJшL|шúf^ фnLÚi|g¡^ШJ¡^ шóшúgJШl¡^ Ц^шот-ßJШÚÁ npnß лúлbuшq¡лшi|шú fuúr}¡púbp¡ lnLÓúшú hшúшp: PbpL[шó bú op¡úшL|úbp, npnúj L[bpшpbpnLÚ bú 2шhnLJß¡ фnLÚi|g¡ШJ¡, bi|шúл¡ фnLÚi|g¡ШJ¡ úшùu¡únLÚ¡, ú¡p¡ú óшflJU¡ úiuju¡iúnLÚ¡i U uцшhшÚ2шpL|¡ шпшâqшi|шúnLßJШú fuúijfipúbpfiú:
^МшршвЬП фnLÚi|g¡ШJ¡ шóшúgJШ[, óш[uu¡ фnLÚL|g¡ш, bi|шúл¡ фnLÚL|g¡ш, 2шhnLJß¡ фnLÚL|g¡ш, LцшhшÚ2шpi|¡ фnLÚi|g¡ШJ¡ шошâqшi|шúnL-ßJnLÚ
JEL: C02, C20
ünlú|g¡mj¡ mómúgjm[¡ qшrçшфшpр úbó û2mûm|nlpjnlû nlú¡ q¡Lnl-pjmù ïmppbp ¿jnl^bpnlú, úmuúm[npmLbu' LÚLbumq¡Lnlpjmú úbj: «PmpÔpmqnljù úmpbúmL¡|m» ^mupúpmg¡ О^шлы^р m^mqm ïùïbum-qbL¡ú ômûnpmgùb[û t npnßmü úmpbúmL¡|m|mú ^pnljpúbp¡, npnùg 2шp-jnlú ¡p nlpnljù ïbrçû nlú¡ $nlú|g¡mj¡ mómúgjm[¡ qшrçшфшpр:
0¡Lmp|búj y=f(x) $nlú|g¡mú, npp npnß[mö t npUt X ú¡2m|mjjnlú, U x0EX: Übpúnlóbúj hbïUjm[ üßmüminlüübpp' Ax=x-x0 (mpqnlúbúL¡ Ш0), ky=¥=f(x+xo)-f(xo) ($nlú|g¡mj¡ Ш0):
0U»b0UShMUMUb SbSbUUO-hSnhra-Snhb 141
Ohmmp^bOp hbmLjm[ umhdmOp'
r
lim —:
Ax^O Ax
Urnhdmbrnd 1: bpb qnjmpjnLO nLOh (ibpjminp ^md mOibpj) ^hmmp^-4n^ umhdmO, m^m mjO ^niinLd t y=f(x) ^nLO^ghmjh mdmOgjm[ x0 ^bmnLd L O2mOm^4nLd t f'(x0) uhdin[ni
f (x0) = lim---,
Ax^O Ax
^md
fix)-fjx0) : 1
/'(x0) = limx
hOi^bu qhmbOp, ^nLO^ghmjh dmpuhdnLdh L dhOhdnLdh ^bmbpp L tpu-mpbdnLdObpp qmOb[nL ^O^hpp nLunLdOmuhpinLd t $nLO^ghmjh mdmOgjm[h d^jngni: 3Lm^bp^bOp tpumpbdnLdObp qmOb[nL mrcmjhO L bp^pnp^ ^mOnO-Obpp:
tpumpbdnLdObp qmbbinL unughO ^mDnOp:
OhgnLp' f(x) $mO^ghmO ^h$bpbOgb[h t (nLOh ibpjminp mdmOgjm[) (x0S, x0+S) dhsm^mjpbpnLd, hu^ x0 ^bmnLd mOpO^hmm t: Uj^ ^b^pmd'
1. bpb f'(x0)>0, bpb
xE( xq—S, xq) L f'(xo)<0, xE(x0, xo+S), m^m x0 ^bmp dmpuhdnLdh ^bm t:
2. bpb f'(x0)<0, bpb
xE(xq—8, xq) L f'(xo)>0, xE( xq, xo+S), m^m xq ^bmp dhOhdnLdh ^bm t:
3. bpb f'(x0)-p O2mOp ih ^n^nLd (x0—S, x0) L (x0, x0+S) dh2m^mj-pbpnLd, m^m x0-O tpumpbdnLdh ^bm it:
tpumpbdnLdObp qmbbinL bp^pnpq ^mbnb^:
OhgnLp' f'(x0)=0, L x0 ^bmrnd f(x) ^nLO^ghmO nLOh bp^pnp^ L|mpqh ibp-jminp mdmOgjm[: Uj^ ^b^pnLd'
1. bpb f '' (x0)>0, m^m x0 ^bmp dmpuhdnLdh ^bm t:
2. bpb f '' (x0 )<0, m^m x0 ^bmp dhOhdnLdh ^bm t:
Ujdd ObpdnLdbOp npn2 mOmbumqhmm^mO ^pnLjpObp:
UrnhdmOnLd 2: OhgnLp' C(x) ^nLO^ghmO x dhminp m^pmOp mpmm^-pb[nL dm^uh ^nLO^ghmO t: Uj^ ^b^pnLd C'(x0)-O ^Obp^mjmgOh x0 dhminp m^pmOp mpmm^pb[nL umhdmOmjhO dm^up: UmhdmOmjhO dm^uh $nLO^-ghmO dnmminpm^bu hmimump t db^ dhminp [pmgnLghi m^pmOp mpmm^-pb[nL dm^uhO.
C'(xo)^C(xo+l)—C(xo)4:
UrnhdmOnLd 3: OhgnLp' R(x) ^nLO^ghmO x dhminp m^pmOp mpmm^-pb[nL ^mpmqmjnLd ummgimd b^mdmh $nLO^ghmO t: Uj^ ^b^pmd R'(x0)-O ^Obp^mjmgOh x0 dhminp m^pmOp mpmm^pb[nL ^b^pnLd umhdmOmjhO b^m-dnLmp: UmhdmOmjhO b^mdmh $nLO^ghmO dnmminpm^bu hmimump t db^ dhminp [pmgnLghi m^pmOp mpmm^pb[nL b^mdmhO'
R'(xo)~R(xo+l)-R(xof:
1 Sb'u ^.lu. UnLunjimG, lJmpbdmmhl|ml|mO mOm[hq, dmu 1, 2009, t2 93:
3 Sb'u OnLjO mb^p., t2 124:
3 Sb'u OnLjO mbr^p., t2 125:
4 Sb'u Hoffman L.D., Bradley G.L., Calculus for Bussines, Economics and Social and Life Scineces, McGraHill 2010, t2 156:
Urnhdmbrnd 4: OhgnLp' P(x) $nLOlghmO x dhminp m^pmOp mpmm^-ph[nL ^mpmqmjmd ummgimd 2mhnLjph ^mO^g^mO t: Uj^ ^b^pnLd P'(x0)-O lObplmjmgOh x0 dhminp m^pmOp mpmm^pb[nL ^b^pnLd umhdmOmjhO 2mhnLjpp: UmhdmOmjhO 2mhnLjph $nLOlghmO dnmminpm^bu hmimump t dbl d|minp Lpmgmgfa m^pmOp wpmw^pb[nL 2mhnLjphO'
P'(xo)^P(xo+1)-P(xo)6:
OpfiQiulj 1. bOpm^pbOp' mpmm^pn^p hm2imp^b[ t, np x d|minp m^pmOp mpmm^pb[nL hmdmp dm^uh $nLOlghmO InLObOm hbmLjmL mbupp'
C(x) =-x2 + 7x +65, L mj^ OnLjO pmOmlni mpmm^pb[nL ^b^pnLd qfOp
4-
llLhOf p(x) =±(100 + x):
^mhmO24nLd t qmObL umhdmOmjhO dm^uf L umhdmOmjhO blmdmh ^nLOlgfmObpp, 10-p^ dfminp m^pmOp mpmm^pbLnL dm^up L blmdnLmp:
UmhdmOmjhO dm^uf ^nLO^gfmO qmObLnL hmdmp mdmOgbOp C(x) ^nLOlgfmO'
C'(x) = ^x + 7:
10-p^ dhminp m^pmOph umhdmOmjhO dm^up 9 dhminp m^pmOp mpmm^pbLnL ^b^pnLd dbl dhminp LpmgnLgfa m^pmOp mpmm^pbLnL umh-dmOmjhO dm^uO t: <m24bOp'
C'(9) = ^ + 7 = 11.5,
npp lObplmjmgOh 10-p^ dhminp m^pmOp mpmm^pbLnL umhdmOmjhO dm^up:
MmqdbOp b^mdmh $nLOlghmO'
fi(x)2xp(x) = ^x(100 + x) = ^x2 + 50x:
UmhdmOmjhO blmdmh $nLOlghmO ImqdbLnL hmdmp mdmOgbOp blmd-mh ^nLOlghmO'
fl'(x) = x + 50 :
¿h2m OnLjO ^mmn^nLpjnLOObpni, hO^bu umhdmOmjhO dm^uh ^b^pnLd, 10-p^ dhminp m^pmOp mpmm^pbLnL umhdmOmjhO blmdnLmp lhm2ibOp hbmLjmL ibp^'
R'(9)=59:
Op/iOiuli 2. bOpm^pbOp~ mpmm^pn^p hm2implbL t, np x dhminp m^pmOp mpmm^pbLnL ^b^pnLd 2mhnLjph $nLOlghmO InLObOm hbmLjmL mbupp'
1
P(x) = ~3x3 + 15x2 - 200x - 300:
^mhmOjinLd t qmObL'
1. umhdmOmjhO 2mhnLjph $nLOlghmO,
2. umhdmOmjhO 2mhnLjpp' x=15 L x=25 mpdbpObph ^b^pmd: UdmOgbOp umhdmOmjhO 2mhnLjph $nLOlghmO'
P'(x) = -x2 + 30x - 200:
5 Sb'u Hoffman L.D., Bradley G.L., Calculus for Bussines, Economics and Social and Life Sciences, McGraHill, 2010, t? 157:
6 Sb'u OnLjO mb^p:
IJUÂblJUSh4U4Ub SbSbUUQhSni-Â3ni-b 143
liÇùÇ 2шhnLJpÇ фnLÛlgÇшû:
UáшûgJШ[Ç ú»2 ш»^ш^п»1пЦ x=10' ^итшйшйр P'(15)=25>0: ётш-пп uшhúшûшJÇû 2шhnLJpp ^пш^шй t, Çù^p пп 16-п^ й^ш-
Цпп шщпшûù шптш^п»[п rçb^pnLÙ 2шhnLJpp 25 ^шЦпппЦ: ÔÇ2m
ùпLjù 1»пщ P'(25)=—75<0, Çù^p lÛ2ШÛшlÇ 26-п^ ^шЦпп шщпшûù шп-^b^pnLÚ lù^qÇ 75 ^шфппЦ:
Ujdú шûrçпшrçшRûшûù ШJûщÇuÇ hшпgbпÇ, nпnûù Ц»пшр»п™й bù b^ùmÇ, 2шhnLJpÇ ^puÇ^^g^ùp U ^ËuÇ фnLÛlgÇшJÇ ùÇùÇ^^g^-ùp: ^шшп^р oпÇûшlûbпp.
OpfiCiuili 3. bûpш^пbûù, шпшш^пп^р 1ш2Цшп1»[ t, пп x ^шфп шщпшûù шптш^п»[п 1шйшп ^ËuÇ фnLÛlgÇшû lnLÛbûш mbupp'
12
С(х) = +Х + 65, U ШJ^ ùnLjù ùшûшïnЦ шптш^п»[п qÇùp l[Ç-
ùÇp(x)=50—3x: ^h^ùçÎnLÙ t qmùb[ шпmшrçпшûùÇ ШJû úÇшЦnпp, nпÇ щш-ПшqшJnLÚ ïéçùç ^puÇ^i 2шhnLJp:
hù^bu qÇrnbùp, 2шhnLJpÇ фnLÛlgÇшû lûbпlшJшgûÇ ш^т-
pjnLùp'
P(x)=R(x)-C(x),
ппш»^
R(x)=xp(x):
^qùbùp 2шhnLJpÇ фnLÛlgÇшû,
7
p(x) = ~2%2 + 45x - 65
U шáшûgbûù ШJû,
P'(x) = -7x + 49:
Îumшûшûù, пп P'(x)=0, »пр x=7: Oqm4»[n4 tрumпbûnLÚ qmùb[nL »п^ппп^ ^ùnùÇg' Цит^шр P"(7)=—7<0: Цbп2Çûu Û2ШûшlnLÚ t, пп x=7-p ^puÇùnLÙÇ l»m t:
OpfiCnulï 4. bûpшrçпbûù, шпшш^пп^ 1ш2Цшп1»[ t, пп x ^шЦпп шщ-Пшûù шптш^п»[п 1шйшп ^ËuÇ фnLÛlgÇшû lnLÛbûш mbupp'
C(x)=2x2+ 70x+32: äbmp t щшпqb[, пп ^шфп шп^^ ùÇçÇù
^Ëup ÏlÇùÇ úÇûÇúш[:
0ÇçÇù ^ËuÇ фnLÛlgÇшû lnLÛbûш rnbupp'
Л(х) = — = 2х + 70 + —:
X X
Qrnùbùù ùÇçÇù ^ËuÇ фnLÛlgÇшJÇ шáшûgJШ[p,
32
А'(х) = 2---.
xz
Îumшûшûù, пп A'(x)=0, »пр x=4: ^24»ù£ ùÇçÇù ^ËuÇ фnLÛlgÇшJÇ »п1ппп^ lшпqÇ шáшûgJШ[p U mb^^bù^ x=4:
A'( 4) = ^ = 1>0:
4 J 43
Ümшgшûù, пп ùÇçÇù ^Ëup 4 ^шЦпп шщпшûù шптш^п»[п ïéçùç úÇûÇúш[:
SûmbuшqÇmnLpJШû ùbç lшпUnп ^»п t Ёш^й щшhшÛ2ШпlÇ фnLÛl-gÇшJÇ шßшÔqшlшûnLpJШû qшrçшфшпp: ЪbпúnLábûù щшhшÛ2ШпlÇ шгсшб-qшlшûnLpJШû qш^шфшпp:
UшhúшùnLÚ б: bûpшrçпbûù, шщпшûùÇ x ^шфп qùÇ щшпшqшJnLÚ фnLÛlgÇшû D(x)-ù t: OÇmшпlbûù ШRû¿nLpJnLÛp,
v y D(x) dx
npp ImOimObOp «^mhmO2mp]h mRm6qm]mOnLpjnLO»:
URm6qm]mOnLpjnLOp gnLjg t mmLhu, pb m^pmOph db] mn]nu w^/O hm-dm^mmmu^mO dnmminpm^bu pmOh mn]nuni ^mhmO2mp-
lp7:
Ohmmp]bOp hbmLjmL ophOm]p'
OpOuil]5. bOpm^pbOp' m^pmOph x dhminp qOh ^mpmqmjnLd ^mhmO-2mplh $nLO]ghmO hbmLjmLO t'
D(x)=360-4x: (0<x<90):
^mhmO2inLd t'
1. QmObL ^mhmO2mp]h mRm6qm]mOnLpjmO $nLO]ghmO:
2. <m2ibL mRmdqm]mOnLpjnLOp x=40 dhminp qOh r^b^prnd L db]-OmpmObL mjO:
1. MmqdbOp hbmLjmL mrcO^nLpjnLOp'
„f x dD(x) x d(360-4x) -Ax
E{X) - =--= -:
D(x) dx 360-4X dx 360-4x
Ummgimd $nLO]ghmO ]Obp]mjmgOh ^mhmO2mp]h mRm6qm]mOnLpjmO $nLO]ghmO:
2. <m2ibL mRmdqm]mOnLpjnLOp x=40 dhminp qOh ^b^pnLd'
E(40)=-0.8:
UmmgmOp, np ^mhmO2mp]h mRm6qm]mOnLpjmO $nLO]ghmO hmim-ump t -0.8-h, hO^p O2mOm]nLd t, np m^pmOph qOh 10% pmpdpmgdmO ^b^-pnLd ^mhmO2mp]p ]O4mqh dnmminpm^bu 8%-ni:
Ujdd ^hmmp]bOp ^mhmO2mp]h mRm6qm]mOnLpjmO hbm ]m^4md hbmLjmL qm^m^impObpp:
bOpm^pbOp' m^pmOph x dhminp qOh ^mpmqmjnLd ^mhmO2mp]h $nLO]ghmO D(x)-O t: Ohmmp]bOp hbmLjmL ^b^pbpp'
1. bpb \E(x)\>1, m^m ]mubOp, np ^mhmO2mp]p mrcm6qm]mO t: ^mhmO2mp]h mRm6qm]mOnLpjnLO O2mOm]nLd t, np qOh pmp6-pmgdmO ^b^pnLd ^mhmO2mp]p mn]numjhO mrcmdni w^l/ 2mm ]Oimqh, pmO mj^ qOh mn]numjhO m^O t:
2. bpb \E(x)\<1, m^m ]mubOp, np ^mhmO2mp]p n^ mrcm6qm]mO t: ^mhmO2mp]h n^ mRm6qm]mOnLpjnLO O2mOm]nLd t, np qOh pmp6-pmgdmO ^b^pmd ^mhmO2mp]p mn]numjhO mrcmdni mibLh ph£ ]Oimqh, pmO mj^ qOh mn]numjhO m^O t:
3. bpb \E(x)\=1, m^m ]mubOp, np ^mhmO2mp]p dhminp wrw5-qm]mO t:
^mhmO2mp]h dhminp mRm6qm]mOnLpjnLO O2mOm]nLd t, np qhOp hO^ mn]ni m^h, ^mhmO2mp]p dnmminpm^bu OnLjO mn]nuni ]O4mqh8:
^mhmO2mp]h mRm6qm]mOnLpjnLOp ubpm nLOh 2mhnLjph $mO]-ghmjh hbm: Ohmmp]bOp hbmLjmL ^b^pbpp.
1. bpb wrcw2wp]h $nLO]ghmO mrcm6qm]mO t (\E(x)\>1), m^m qhOp pmp^pmgObLnLg hbmn 2mhnLjpp ]O4mqh:
7 Sb'u Hoffman L.D., Bradley G.L., Calculus for Bussines, Economics and Social and Life Sciences, McGraHill, 2010, t2 249:
8 Sb'u OnLjO mbr^p, t2 251:
UU^blJUShMUMUb SbSbUUO-hSnhra-Srihb 145
2. bpb mrcm2mpLf ^mOLgfimO n^ mrcmdqmLmO t (]E(x)]<1), m^m qfOp pmp6pmgOb[nLg hbmn 2mhnLjpp Lm^fi:
3. bpb mrcm2mpLf $m.O^gfiwO dfminp mrcmdqmLmO t (\E(x)]=1), m^m qOfi pmp^pmgmdp 2mhnLjpf ipm qpbpb ¿f mq^f9:
OfmmpLbOp hbm^jm[ opfOmLp, npp ibpmpbpmd t ^mhmOjmp^l $nLO^g|mj| mrcmdqmLmOnLpjmO pOnLjpfO:
OpfiCuuLj5. bOpm^pbOp' m^pmOpf x dfminp qOf ^mpmqmjnLd ^mhmO-2mpLf ^mOLgfmO hbm^jm[O t'
D(x) = 1200 -x2: (0 <x<Vl200): ^mhmOjinLd t ^mpqb[, pb $mOLgfmO bpp t mrcmdqmLmO, n^ mrcmdqm-LmO, d|minp mrcmdqmLmO, L mj^ ^b^pbpnLd fO mq^bgmpjnLO t [fOnLd 2mhnLjp| $nLOLg|mj| ipm:
MmqdbOp ^mhmOjmpL! mrcmdqmLmOnLpjmO ^mOLgfimO' x dD(x) _ x d(1200 -x2)_ -2x2 W ~ D(x) dx ~ 1200 -x2 dx _ 1200 -x2: ^mhmOjmpL! mrcmdqmLmOnLpjmO pOnLjpp ^mpqb[nL hmdmp ^mhmO-2mpL| mrcmdqmLmOnLpjmO $nLOLgfmjf dn^nL[p hmimumpbgObOp 1-f:
—2x2
2x2 _
1200 -x2 _1 _ 0:
MummOmOp, np'
2x3 - 1200 _
1200 — x2 ~ : LnLdb[ni ummgimd hmimumpnLdp' LummOmOp, np x=20: OfmmpLbOp hbm^jm[ bOpm^b^pbpp.
1. bpp x=20 ^mhmOjmpL! $mOLgfmO dfminp mrcmdqmLmO t: Uju ^b^pnLd 2mhnLjp| ^mOLgfimO dOnLd t qpbpb OnLjOp:
2. bpp 0<x<20, m^m ]E(x)]<1, mjufiOpO' ^mhmOjmpLf ^mOLgfmO mrcmdqmLmO t: Uju ^mpmqmjnLd qfOp pmp6pmgOb[nLg 2mhnLjpf ^mOLgfmO LOimqf:
3. bpp 20 < x < 20V3, m^m ]E(x)]>1, mjufOpO' ^mhmOjmpLf gfmO n^ mrcmdqmLmO t: Uju ^mpmqmjnLd qfOp pmp6pmgOb[nLg 2mhnLjpf ^nLOLgfmO LO4mqf:
«PmpdpmqnLjO dmpbdmmfLm» ^mupOpmgfi ^mumimO^dmO dmdmOmL dbL ^n^n^mLmOf $nLOLgfimjf mdmOgjm[p nLunLdOmufpb[|u LmpLnp t nLOLO^pfO OjnLpp ^fium dmpbdmmfLmLmO m^mgnLjgObpni dmmmgb[p: QnpdOmLmO ^mumdmdbpfO dbL ^in^n^mLmOfi $nLOLgfmjfi mdmOgdmO mb^OfLmjfO 6mOnpmgOb[nLg hbmn oqmmLmp LlfOf ObpLmjmgOb[ mjO^fuf ^O^fpObp, fiO^fufp ^fmmpLimd bO mju m2^mmmOpnLd: Uju pOnLjpf ^O^fpObpp Lmpn^ bO ^pmOb[ m^mqm mOmbumqbmf hbmmppppnLpjnLOp' mpmib[ O^mmmLm^pimd uninpb[nL «PmpdpmqnLjO dmpbdmmfLm» ^mu-pOpmgp, pmOf np mOmbumqfmmLmO npn2 ^O^fipObpf [rnddmO hmdmp oq-mmqnpdinLd bO dmpbdmmfLmLmO dbpn^Obp:
1200 -x2
2x2
9 Sb'u Hoffman L.D., Bradley G.L., Calculus for Bussines, Economics and Social and Life Sciences, McGraHill, 2010, t? 252:
Oqmmqnpdirnd •ршЦшйт^т.й
1. UnLun^Oi 4.Ю., ш&ш^, ¿¡ши 1, bp., 2009:
2. QLnpq^Oi Q.Q. L mp^Cibp, 0ш|эЬ^шт|-|1|ш1|ш[| ш[|ш[|^|1 Ё^^рш-qhpp, bp., 2014:
3. Фихтенгольц Г.М., Курс дифференциального и интегрального исчисления, том (2), 2001.
4. Hoffman L.D., Bradley G.L., Calculus for Bussines, Economics, and Social and Life Sciences, McGraHill, 2010.
uuÂbiJusbîUîUb sbSbuuo-bsriïÂsriïb 147
ГАИК КАМАЛЯН
Ассистент кафедры высшей математики АГЭУ, кандидат физико-математических наук
Методы решения некоторых задач экономического характера с применением производной одной переменной в рамках курса высшей математики.- Работа посвящена использованию производной функции одной переменной некоторых экономических проблем. В работе приведены примеры касающиеся задач функции прибыли, максимума функции дохода, минимума средних затрат и эластичности спроса.
Ключевые слова: производный функции, функция стоимости, функция дохода, функция прибыли, эластичность спроса.
иЕ1_: С02, С20
HAYK KAMALYAN
Assistant Professor at the Chair of Higher Mathematics, PhD of Mathematics
Methods of Solving Some Economic Problems by Using One Variable Derivative in the Course of Higher Mathematics.-
The paper touches upon the application of one variable function derivative for solving some economic problems. The work provides examples referring to the problems related to profit function, revenue function maximum, average cost minimum and demand elasticity.
Key words: derivative of a function, cost function, revenue function, profit function, elasticity of demand. JEL: C02, C20
