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?