Applied Mathematics for Business and Economics

Lecture Note Differentiation

14 cUrrktémøRbEhlénbMErbMrYlCaPaKryrbs;GnuKmn_fx x( )=^2 +− 29 x eBlxekIn

eTA4.3. (Estimate the percentage nction

B

change in the f

I 4

u fx x( )=^2 +− 29 x a

increa es f 4

s x

s rom to 4.3.)

15 cUrrktémøRbEhlénbMErbMrYlCaPaKryrbs;GnuKmn_ ()

2

fx 3 x

x

= + eBl xfycuHBI

nction

5

eTA 4.6. (Estimate the percentage change in the fu (^) ()

2

fx 3 x

x

= s

de se

16

+a x

crea s from 5 to 4.6.)

éføedImsrubrbs;plitkrmñak; KWCq( )=−++0.1q^32 0.5q 500 q 200

W4ÉktaehIypl

duløaenAeBlEdl

enaHeRKagnwg

b k srub. (A

manufacturer’

kMritplitkmμesIμnwgqÉkta. kMritcrnþrbs;plitkmμK itkr

egáIn[)an4/1É a. ):an;sμan b¤rktémøRbEhlénTMhMbMErbMrYlrbs;éføedIm

s total cost is

t

( )

Cq=−0.1q^3 0.5q^2 ++ 500 q 200 dollars when the

production is 4 units, and the

crease this to 4.1 units. Estimate

17

nt by

e current

value of the variable is

18

level of production is q units. The current level of

manufacturer is planning to in how the total cost

will change as a result.) (Answer: $50.08)

eKrMBwgTukfatqñaMeTAmuxeTot cracrN_énsarBt’mankñúgRsukmYykMNt;eday

Ct()=++ 100 t^2400 t5, 000.

rktémøRbEhlénbrimaNkMeNIncracrN_sarBt’mankñúgkMlug6 ExbnÞab;. ENnaM³

témøcrnþénGefrKI t= 0. (It is projected that t years from now, the circulation of a

local newspaper will beCt()=++ 100 t^2400 t5, 000. Estimate the amou

which the circulation will increase during the next 16 months. (Hint: th

t= 0 ). (Answer: 200)

karsikSaelIbrisßanenAkñúgshKmn_mYy)anelIeLIgfa ry³eBltqñaMBIeBlenHeTAmux

kMritCamFümén kabUnm:UNUGuksuItenAkñúgxül;esμInwg Qt( )=++0.05t^2 0.1t3.4PaK

kñúgmYylanPaK. etIenAkñúgkMlug6 Exxagmux kMritkabUnm:UNUGuksIutnwgERbRbYlRbEhl

b:unμan? (An environmental study of a certain co years

he

g 6 months? ) (Answer: 0

19

mmunity suggests that t

from now, the average level of carbon monoxide in the air will be

Qt()=++0.05t^2 0.1t 3.4parts per million. By approximately how much will t

carbon monoxide level change during the comin .05

parts per million)

karsikSaelIRbsiT§PaBkargarénevneBlRBwkenAkñúgeragcRkmYy)anbBa¢ak;fa CamFüm

kmμkrEdlmkdl;kEnøgeFVIkarenAem:ag8³00nwgRbmUlviTüú)anf(xxx)=− + +^32615 x

kñúgry³eBlxem:agbnÞab;. etIkmμkrenaHRbmUlviTüú)anRbEhlb:unμankñúgcenøaHBIem:ag