Applied Mathematics for Business and Economics

Lecture Note Differentiation

K> etIkmμkrenaHRbmUlCak;Esþg)anviTüúb:unμaneRKOgcenøaHBIem:ag 9³00

eTAem:ag10³00RBwk?

(An efficiency study of the morning shift at a certain factory indicates that an

average worker who arrives on the job at 8:00 A.M. will have a

()

ssembled

f xx=−^32615 e a formula for the rate at which the worker wil

be assembling radios after x hours. b/. At what rate will the worker be assemblin

radios at 9:00 A.M.? C/. How many radios will the worker actually assemb

between 9:00 and 10:00 A.M.?)

+ +x x. a/. Deriv l

g

le

(a/.fx′()=− + + 3121 x^2 x 5 , b/. 24 Radios per hour, c/.26)

5 rkGRtaERbRbYlPaKryénGnuKmn_ f(ttt)= 372 −+ 5 eFobeTAnwg teBl. (Find

the percentage rate of change in the function

t= 2

f(tt)= 372 −+t 5 with respect to t ,

when t=2.

6 rkGRtaERbRbYlPaKryénGnuKmn_ () ( )eFobeTAnwg
2
fx xx=+ 3 xeBl. (Find

the percentage rate of change in the function with respect to

x= 3

fx()=+xx( (^3) )
2
x,
whenx= 3 .) (Answer: 66.67 percent)
7 eKTsSn_TayfaxExxagmux GRtaRbCaCnrbs;TIRkugmYyesμInwg
()
Px=+ +24 5,00x x^320.
k> etIGRtaRbCaCnnwgERbRbYlkñúgGRtab:unμankñúgeBl9Exxagmux?
x> etIGRtaRbCaCnnwgERbRbYlkñúgGRtab:unμanPaKry kñúgeBl9Exxagmux?
(It is projected that x months from now, the population of a certain town will be
Px()=+ +24 5,00x x^32 0. a/. At what rate will the population be changing with
respect to time 9 months from now? b/. At what percentage rate will the
population be changing with respect to time 9 months from now?)
8 R)ak;cMNUlRbcaMqñaMsrubrbs;Rkumh‘unmYy KW At( )=0.1t^2 ++ 10 t 20 Ban;duløa ry³eBl
tqñaMbnÞab;BI karbegáItenAkñúgqñaM1987.
k> etIcMNUlRbcaMqñaMsrubrbs;Rkumh‘un nwgekInkñúgGRtab:unμaneFobeTAnwgeBlenA
kñúgqñaM1991?
x> etIcMNUlRbcaMqñaMsrubrbs;Rkumh‘un nwgekInkñúgGRtab:unμanPaKryeFobeTA
nwgeBl enAkñúgqñaM1991?
(The gross annual earnings of a certain company were At( )=0.1t^2 ++ 10 t 20
thousand dollars t years after its formation in 1987. a/ At what rate were the gross
annual earnings of the company growing with respect to time in 1991? b/. At
what percentage rate were the gross annual earnings of the company growing
with respect to time in 1991? ) (a/. 10,800 people, b/.17.53 percent).