Applied Mathematics for Business and Economics

Lecture Note Differentiation

x> etIenAkñúgExmkraqñaM 1992 ;cMNUl rub rbs;Rku

p ere ()

R)ak s mh‘unnwgekInkñúgGRtab:unμan

PaKry?

(The gross annual earnings of a certain com any w ft=++ 10 t t^2236

thousand dollars t years after its formation in January 1988. a/. At what rate were

any growing in Janua /. At what

earnings growing in January 1992? (a/.

34 kar

mF

the gross annual earnings of the comp ry 1992? b

percentage rate were the gross annual

$2,025 per year, b/.10.125 percent per year.)

sikSaelIRbsiT§iPaBkargarevneBlRBwkenAkñúgeragcRkmYy)anbgðaj[eXIjfaCa

ümkmμkrEdlmkdl;kEnøgeFVIkargarenAem:ag8³00 nwgplit)an

Qt( )=− + +t^32815 t t

ÉktaenAtem:agbnÞab;.

mμenArbs;kmμkrenAem:ag 9³00RBwk.

x> etIkñúgGRtab:unμanEdlGRtaplitkmμrbs;kmμkrERbRbYleFobeTAnwgeBl

k> KNnaGRtaplitk

ak;EsþgénGRtaplitkmμrbs;kmμkrenAkñúgcenøaHBIem:ag9³00

(A ctory indicates that an

av produced

s rate of

production at 9:00A.M. b/. At what rate is the worker’s rate of production

ch change

in ute the

actual change in the worker’s rate of production between 9:00 and 9:15A.M.)

35 Su

is

a. roduction is the average cost per unit the smallest?

enAem:ag9³00RBwk.

K> ):an;sμanTMhMbMErbMrYlénGRtaplitkmμrbs;kmμkrenAkñúgcenøaHBIem:ag9³00

eTAem:ag9³15.

X>KNnaTMhMbMErbMrYlC

eTAem:ag 9³15.

n efficiency study of the morning shift at a certain fa

erage worker who arrives on the job at 8:00AM. Will have

Q()t=− + +t^328 t 15 t units t hours later. a/. Compute the worker’

anging with respect to time at 9:00A.M? c/.Use calculus to estimate the

the worker’s rate of production between 9:00 and 9:15A.M. d/. Comp

ppose the total cost in dollars of manufacturing q units of a certain commodity

Cq()=++ 3575 q^2 q.

At what level of p

b. At what level of production is the average cost per unit equal to the

marginal cost?

]bmafaéføedImKitCaduløaelIkarplit qÉktaénmuxTMnijmYyRbePTKWCq( )= 3575 q^2 ++q.

k> etIkMritplitkmμ qesμIb:unμanEdleFVI[GnuKmn_cMNaymFümkñúg1Ékta tUcbMput?

x> etIkMritplitkmμ qesμIb:unμaneTIbGnuKmn_cMNaymFümkñúg1ÉktaesμInwgGnuKmn_cMNaym:aCIn?