Lecture Note Differentiation
h. yxx=− +20 4(^2 )( (^21) ) i. (^) () ()^32
1
21
5
fx= x−+xj. fx()=− (^35) (x^3 − +2 4x ) k.
23
54
x
y
x−
=
+
l. ()3
3
fx
x=
+
2 rkGRtaERbRbYlénGnuKmn_f(x)eFobeTAnwg xcMeBaHtémøxEdleKbBa¢ak; (Find the
rate of change of the given functionf(x)with respect to x for the prescribed
value of x. )a.fx x x()=−+ =^3 35, 2x , b. fx( )= x xx+=5, 4
c.fx()=+ + =()x^2 2,()x x x 4 d.f(xx)=(^23 +− =352 , 1)( xx)e. ()
21
,1
35
x
f xx
x−
==
+
f. (^) ()
3
,0
24
fx x x
x= +=
−
3 eKrMBwgTukfakñúgry³eBltqñaMKitBIeBlenHeTA cracrN_énsarBt’mankñúgRsukmYynwg
esμIeTAnwg Ct()=+ 100 t^2400 t+5, 000.
k> cUrTajrkenSammYyEdltag[GRtabMErbMrYléncracrN_sarBt’maneFobeTAnwg
eBlt.
x> etIcracrN_sarBt’mannwgERbRbYlkñúgGRtab:unμaneFobnwgeBlkñúgry³eBl5qñaM
BIeBlenH eTA? etIenAeBlenaHcracrN_sarBt’man ekIneLIg b¤Føak;cuH?
K> etIenAqñaMTI6 cracrN_sarBt’mannwgERbRbYlCak;EsþgkñúgTMhMb:unμan?
(It is estimated that t years from now, the circulation of a local newspaper will be. a/. Derive an expression for the rate at which the
circulation will be changing with respect to time t years from now. b/. At what
rate will the circulation be changing with respect to time 5 years from now? Will
the circulation be increasing or decreasing at that time? c/. By how much will the
circulation actually change during the 6th year?)
Ct()=++ 100 t^2400 t5, 000(a/.Ct′()=+ 200 t 400 ,b/.Increasing at the rate of 1,400 per year, c/. 1,500)4 karsikSaGMBIRbsiT§PaBkargarevnRBwkenAkñúgeragcRkmYy)anbgðaj[eXIjfa CamFüm
kmμkrEdlmk dl;kEnøgeFVIkarenAem:ag8³00RBwk n
()(^3261)
wgRbmUlviTüú)ancMnYn
f xxx=− + + 5 xkñúgry³eBl xem:ag bnÞab;.
k> TajrkkenSammYytag[GRtaénkarRbmUlviTüúrbs;kmμkr
bnÞab;BI)ancab;epþImkargarry³eBl xem:ag.
x> etIGRtaénkarRbmUlenAem:ag9³00esμInwgb:unμan?