Applied Mathematics for Business and Economics

Lecture Note Differentiation

9 tamry³kMNt;Rta)anbgðajfa kñúgry³eBlxqñaM bnÞab;BIqñaM1985eTA Bn§elIkmμsiT§i Ca

mFümcMeBaHpÞH EdlmanbnÞb;3 enAkñúgshKmnmYykMNt;edayGnuKmn

Tx()=++ 20 x^240 x 600.

k> etIBn§elIkmμsiT§iekInkñúgGRtab:unμaneFobeTAnwgeBl enAkñúgqñaM1991?

x> etIBn§elIkmμsiT§i ekInkñúgGRtab:unμanPaKry eFobeTAnwgeBl enAkñúgqñaM1991?

(Records indicate that x years after 1985, the average property tax on a three-bedroom

home in a certain community was Tx( )=++ 20 x^240 x 600. a/. At what rate was the

property tax increasing with respect to time in 1991? b/. At what percentage rate was the

property tax increasing with respect to time in 1991?)

10 μanfatqñaMeTAmuxeTotGRtaRbCaCnenAkñúgTIRkugmYynwgesμIeTAnwg

()

t t=+ +^2200 10, 000.

eK):an;s

(It i

f

in

P t

k> sresrkenSammYytag[GRtabMErbMrYlPaKryénGRtaRbCaCnCaGnuKmn_én

rYcsg;RkahV.

etIenA kñúgry³eB

t

x> lyUreTAxagmuxeTotGRtabMErbMrYlPaKryenHeTACay:agNa?

s estimated that t years from now, the population of a certain town will be

()

Pt t=+ +^2200 t10, 000. a/. Express the percentage rate of change of the

pop t, simplify this function algebraically, and draw it

graph. b/. What will happen to the percentage rate of change of the population

the long run? ) (a/.

ulation as a function o

20

percent, b/. 0)

t+ 100

11

2

plTunCatisrubrbs;RbeTsmYyekIneLIgkñúgGRtaefr. enAkñúgqñaM1986 plTunCatisrub

esμInwg 125 Ban;landuløa ehIyenAqñaM1988 plTunCatisrubesμInwg155Ban;landuløa.

etIenAkñúgqñaM1991 plTunCati srubnwgekIneLIgenAkñúgGRtab:unμanPaKry? (The gross

national product (GNP) of a certain country is growing at a constant rate. In 1986

the GNP was 125 billion dollars, and in 1988 the GNP was 155 billion dollars. At

what percentage rate was the GNP growing in 1991? ) (Answer: 7.5 percent)

1 cUrrktémøRbEhlénTMhMERbRbYlrbs;GnuKmn_fx x( )=^2 −+ 35 x ebIxekInBI5 eTA

5/3. (Estimate how much the function f(x x)=^2 −+ 35 x will hange as x

increases from 5 to 5.3.) (Answer: 2.1)

c

3 cUrrktémøRbEhlénTMhMERbRbYlrbs;GnuKmn_ () 3

1

x

fx

x

= −

+

ebIxfycuHBI eTA.

(Estimate how much the function

4 3.8

()^3

1

x

fx

x

= −

+

will change as x

from to )

decreases

4 3.8

1