Applied Mathematics for Business and Economics

Lecture Note Differentiation

28 enAkñúgeragcRkmYy plitplRbcaMéf¶KW QK( )= 1 12 EdlKtag[vinieyaK

mUlFnrbs;Rkumh‘un. ):an;sμankMeNInCaPaKryénvinieyaKmUlFnEdlRtUvkar edIm,IbegáIn

plitpl 1.2PaKry. (At a certain factory, the daily output is ()

, 200K Ékta

QK=1, 200K^12

units, where Kdenotes the firm’s ent. Estimate the percentage

increase in capit investment that is needed to produce a 1.2 percent increase in

output.)

capital investm

al

9 ]bmafaéføedImsrubKitCaduløaelIkarplitqÉktaKWCq( )=++ 3 q q^2500.

:an;sμanéføedImelIk a

ar

2

k> eRbIkarviPaK m:aCINl edIm,I) arplitÉkt I 41.

x> KNnaéføedImCak;EsþgelIkarplitÉktaTI 41.

(Suppose the total cost in dollars of manufacturing q units is

00. a/. Use m ginal analysis to estimate the cost of

manufacturing the 41th unit. b/. Compute the actual cost of manufacturing the

41th.)

T

Cq()=++ 3 q q^25

30 éføedImsrubrbs;plitkrmñak;kMNt;edayCq( )=0.1q^32 −++0.5q 500 q 200 duløa

Edl

k Ik itÉktaTI 4.

manufacturer’s tota

qCacMnYn ÉktaEdlRtUvplit.

eRbIkarviPaKm:aCINl edIm,I):an;sμanéføedIm,Iel arpl

x> KNnaéfø edImCak;EsþgelIkarplitÉktaTI4.

(A l cost is Cq( )=−++0.1q^32 0.5q 500 q 200 dollars,

q is the number of units produced. a/. Use marginal analysis to estimate the cos

of manu

where

t

facturing the 4th unit. b/. Compute the actual cost of manufacturing the

th

31 erivative

4 unit.)

Use the chain rule to compute the d

dy

dx

and simplify your answer.

a.yu u x=^2 +=−1, 3 2 b.yuu u x=25,1^22 −+ =−

c.yuux x= ,23=+−^2 d. 2 2

1

yu,

u

= =+x (^1)
e.yux^1 ,9^22 ,^1
u
= =− f.
1
yuu
x

==

−

ifferentiate the following function

/. ()

32 D

a 2

1

41

fx

x

=

+

b/. ()

()

2 4

3

1

fx

x

=

−

c/. ()( )

5
f xx=+ 13

33 R)ak;cMNUlRbcaMqñaMsrubénRkumh‘unmYyKWft()=++ 10 t t^2236 Ban;duløa kñúgry³eBl

qañM eRkayBI karbegáItenAkñúgExmkraqñaM 1988.

k> etIenAkñúgExmkraqñaM 1992 R)ak;cMNUlsrub rbs;Rkumh‘unnwgekInkñúg GRtab:unμan?

t