Class
Meeting
#17
Example
Problems
l)
Find
the
intervals
on the
x-axis
for
which
the following
curve
is
concave
up &
concave down.
Find
all
points
of
inflection
&
make
a
careful sketch
of the curve.
f(x)=x'-9x'-43a+52
(
**.t
)
rta
aa,,ryh-4
l..,-tcc'L
h/t/*-
{"(*)<a
Sat
b*-tg€o
-1>
6Yctt
+
'c<''
fia-
W
*'#
h'Z'"*{a(x!=o
So,
CY-t|?o
+
*=3'
4-*
'*J4'
d(s)
s
-/4L
SKAI.:
2)
Find the
point
of
diminishing
returns for
the revenue function
R(x)
=
-
(x-3)
4
+
6(x-3)3
+60(x-3)
2
-z1x-S;
-50.
Make a
caretul sketch
of the curve
ffi
,:$7J#i'7
ffi
, E
€,
{x-s)
-
?
R,{x)
=
-tz
{x-r)a*
g6{x-r)*
tzo
R',/x\=o
+
-ta{x-E)a+-3&{x-Y'i*/zo
E
A
{x*3}e
-3{x*s}
'la=&
Yz*?x
+F*4
+
Ct-r){x*glao
fu
p=
t
r
k*8r
C.r,44-
uL
Ri'/*\-'-t"'G*
F*'=
,
4
?T**tr
.y-tta-L
Yn-L*,*,,*
Lo*1't-,*A
lLet
+
z"i?
,Je=xt
a
a/a.*7+-'"**"**p'
t*':
"*
U
-
',
ys
7,8-l*9
Et'dzrs)>'J+
;
Sbal-,:
T*
pro{
+
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yef.2eil,o
X-*
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l,
at
+ l?
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g
a*{6;*
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gr
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e
t.2e1
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Teitio;
tu'J
