Week ln Review #8
Novembe r 2, 2015
5. Suppose the derivative of a function is
f '(x)_ (x + Z)'(x - 1)t (x - B)n . on what
interval(s) is the function increasing?
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1,. Use the graph to state the absolute and local
maximum and minimum values of the function.
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2, Find the critical numbers of the fu nctio n:
f(x): lax-61 = {
Q}c-6, Xlo
l*- { y *b, x((}
Yz-1, S
6. Find the exact value at whi ch f (x) :
ranidrY'
lf imost
$t ? -?
"S't
Find the critical numbers of the function:
f (x) - x3 + 6x2 - LSx
J' = sy*+ tL>e*rfl s.#
x- * qv ""ffs #
(v *SXX *,)*P
Ir*S'\ K*f
t*\***{e}&
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fr
3.
e-x
x'2
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7
. consider
domain of
f
a fun.,ionTriat ii^-d^b"'fr't*ilo,i, on its
(-m,
'(x):m
ll " (i. *1. Atso
and
f
"(x):#.
Find
where any local maximum and minimum values
of
4,
Find the intervals of increase or decrease,
loca I max/m in va lues, interva ls
of concavity a nd
f (x)
occur.
$,*o \,2#ffir{*?x#}
LySt)- #2.\ rct
points of inflection.
f (x) : xt/z (x + 4)
,Xr*n
9t = &/3{,) *(x+./)(# iYt
3'= N'ts + t Fol# riL f%
2{E #
;;
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vn * #
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}
w{x'};
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8. The sum of two number is 42, what is the
smallest possible value of the sum of their
squares?
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l-0. A rectangular storage container with an
open top is to have a volume of j.2 m3. The
length of the base is twice the width. Material
for the base costs SS per square meter, and
material for the sides costs $S per square
meter. Find the minimum cost of such a
z
S ax?-tlrt a*{*se{. 1*+-f U*4:-'*Y
$ 7 Zv*o, k rt x" -e-l?*4
$n = L{ y ',"*8{ *O
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4yx-f 4, v*?l
bor",.reryua o*'f
h='}"-
ftrt'(.1.L*"
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lL{ F"{
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z lD ,^Je-.f-
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=tb
(-+
f '(x):&
t0
,f
/1 --2
* lb
\-'
"(x): ffi
Determine the intervals of concavity.
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t\z+
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9. Consider a function that is continuous
everywhere.
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