(,'1
(::· 211()
-, z. ' ,~ ➔ unit 3 ·.H.. q)t.~l~.
l,/ n, t
(/ 0
, le, I ,.
un;t 3.l
➔ uni t-
.,
J,5 ➔
c;-:
(.;
)J' . '
l '' 3.:3
lo ➔ uni~
~ Uni~ 3 (?;'
0)
➔ Uf'JI~ 3,lJ
➔ u n1 r u,7.
®4,3 ®
➔ unit l.J . I
➔ U1) I ~
7
0 1.J... hul '"' Sc t C', ,d c.l t' 1, v0 /, c' l '
.~ ,::, a functio n I tF rc:x:.) , ir's ti rst;; deriuor ive. ~,(:t)
I ~
1$ olSo o Fu(')Ction. Thus we wf'1 di fferent: 1 ot"e w,~h rts p ctt
1:.-0 .x:. . We co11 c..h is Gler111a1;ve. the. s~co!\d de r 111 o ri ue. CJ/)d wr, ~e ; t OS
0
Th~01~e rri Let I ' be. c,n 1n t,erual and IC f. ' FI be C& fuf'\Ct: l o I) v..ih osc
s econd I('>
dH1\lO h ,J Q. of ex, sts on I I' 'Then I
'
J. . Ir: ' 1S c. oricau e up on ' 1' r ,, (,".'l..)
iF cind Qr) 13 ;f:' ;, o on I
2 . '(' a:ncu u e 1'
1S d ouJn 01") 1f Qr) d Q('\ It)
' !=-
r "ex) c..o of)
I I'
0
Lccrn1 p lC. 1' F1M.I the 1rit.er ual~ 0 (-' concuu 1~~ For .the graph oF j if:
3 7.
/J:x f '3-x - (ax
X
x. r 3
I 2 r:;1
c) ~-= z .x - --J3 x= f, 2 In x.
s,. 11.<l,11,;,1 ·.
q\
'.J lF LlX
3 + 3 :x: 'Z. -1a:.x. . tl
Hl -:: IZ.. X: '2 I- "':;:c. - b
,,
8 -= -z.u:x. t "'
:x: :: 0 oR
, ii
~ ::. o
-J..
4
g u.1pl!\ oF ,::i con co vc.
-rf\~ -B I.Ip O{)
ao ) ciri d
co n e n ue
I
0 00 (- oC - ~ ),
cl o, '-
:)C
~ ~
b) ::t:: r 3 .. ➔ hrid 'd I
Cx) 1 C-:x: ~ 3) - ::::t:: C.x: ra)
(3
I
-- (?c.t -3)-z . ..;. Find ell
·::t:. r 3 - :z:. ➔ f\lXl'lb er
::
(:X:r .3)z 5 ~etch ~ l i ne
-'2
-= 3C xt3 )
0,1 ~ C3) C-z )(:: :e+ 3)-
3 °' d e l H0"1 1<'i( conca v1~j-
-!o
-3
oi'I __C. :-3 _s:>q_) .. ar-.d c.onc a ve. .
conc ove do(..U 0
(-c,c J. -'3)
up 0() •
'Z
zln x
c) ~ ·-o i~ - J3 X I
-z.
1d
~ ;,:: - Jg1
·7.
~ 'X - -·-· -
~II -:. I - xi
::i:: 7. - z.
= ----
. .:x:;
0 c. ..,,..,q,n ,'2, co I
oo)
8 ";, 0
0
af\cl _ .co nca1.- a..
e. d DLu f\
.. on_
con 00 1..1
, " E
• ••✓.:c,nipl f' z. s~et.c h a f'unct. 1oD
<l) F i<o cant. i f')UO ~ S at-I
co:<o)
6) Frz.) =a o /\d
Fcx) >o ,~ j F-
d)
Col\CCJ u t
dowf\
X
ii,'
0
,·' c.o f'l cave up
·, ......
-yP
Let: F'C:c_) ; x 4 --zx 3 ~
1
j () t e f U O \ $ OF LU I) i C h
'f ' ' S dt C.J.e O S j ne ,
t_h e 1f)tt(UC IIS Oil w h ich - ~ 1S ceif'lco ue up O[)d
cco ccive down .
t-rl e ,n r'orrno \:.i Of) C11'iCl S1l.et;c h the po 1tj nom io I
3, l ) ~- 1 (ac ) ~ Li :,e 3 - lox
2
l,z l ( z. :;c, · 3 )
or 3
?C :; 2.
0 S
2
Fc:x.) isd ecreas1f)B of'\ c-~ : o_)_ ~__ c~ ; 31z) af\d ~C-x) ,s
o0 c31z ; ~) .
(::· 211()
-, z. ' ,~ ➔ unit 3 ·.H.. q)t.~l~.
l,/ n, t
(/ 0
, le, I ,.
un;t 3.l
➔ uni t-
.,
J,5 ➔
c;-:
(.;
)J' . '
l '' 3.:3
lo ➔ uni~
~ Uni~ 3 (?;'
0)
➔ Uf'JI~ 3,lJ
➔ u n1 r u,7.
®4,3 ®
➔ unit l.J . I
➔ U1) I ~
7
0 1.J... hul '"' Sc t C', ,d c.l t' 1, v0 /, c' l '
.~ ,::, a functio n I tF rc:x:.) , ir's ti rst;; deriuor ive. ~,(:t)
I ~
1$ olSo o Fu(')Ction. Thus we wf'1 di fferent: 1 ot"e w,~h rts p ctt
1:.-0 .x:. . We co11 c..h is Gler111a1;ve. the. s~co!\d de r 111 o ri ue. CJ/)d wr, ~e ; t OS
0
Th~01~e rri Let I ' be. c,n 1n t,erual and IC f. ' FI be C& fuf'\Ct: l o I) v..ih osc
s econd I('>
dH1\lO h ,J Q. of ex, sts on I I' 'Then I
'
J. . Ir: ' 1S c. oricau e up on ' 1' r ,, (,".'l..)
iF cind Qr) 13 ;f:' ;, o on I
2 . '(' a:ncu u e 1'
1S d ouJn 01") 1f Qr) d Q('\ It)
' !=-
r "ex) c..o of)
I I'
0
Lccrn1 p lC. 1' F1M.I the 1rit.er ual~ 0 (-' concuu 1~~ For .the graph oF j if:
3 7.
/J:x f '3-x - (ax
X
x. r 3
I 2 r:;1
c) ~-= z .x - --J3 x= f, 2 In x.
s,. 11.<l,11,;,1 ·.
q\
'.J lF LlX
3 + 3 :x: 'Z. -1a:.x. . tl
Hl -:: IZ.. X: '2 I- "':;:c. - b
,,
8 -= -z.u:x. t "'
:x: :: 0 oR
, ii
~ ::. o
-J..
4
g u.1pl!\ oF ,::i con co vc.
-rf\~ -B I.Ip O{)
ao ) ciri d
co n e n ue
I
0 00 (- oC - ~ ),
cl o, '-
:)C
~ ~
b) ::t:: r 3 .. ➔ hrid 'd I
Cx) 1 C-:x: ~ 3) - ::::t:: C.x: ra)
(3
I
-- (?c.t -3)-z . ..;. Find ell
·::t:. r 3 - :z:. ➔ f\lXl'lb er
::
(:X:r .3)z 5 ~etch ~ l i ne
-'2
-= 3C xt3 )
0,1 ~ C3) C-z )(:: :e+ 3)-
3 °' d e l H0"1 1<'i( conca v1~j-
-!o
-3
oi'I __C. :-3 _s:>q_) .. ar-.d c.onc a ve. .
conc ove do(..U 0
(-c,c J. -'3)
up 0() •
'Z
zln x
c) ~ ·-o i~ - J3 X I
-z.
1d
~ ;,:: - Jg1
·7.
~ 'X - -·-· -
~II -:. I - xi
::i:: 7. - z.
= ----
. .:x:;
0 c. ..,,..,q,n ,'2, co I
oo)
8 ";, 0
0
af\cl _ .co nca1.- a..
e. d DLu f\
.. on_
con 00 1..1
, " E
• ••✓.:c,nipl f' z. s~et.c h a f'unct. 1oD
<l) F i<o cant. i f')UO ~ S at-I
co:<o)
6) Frz.) =a o /\d
Fcx) >o ,~ j F-
d)
Col\CCJ u t
dowf\
X
ii,'
0
,·' c.o f'l cave up
·, ......
-yP
Let: F'C:c_) ; x 4 --zx 3 ~
1
j () t e f U O \ $ OF LU I) i C h
'f ' ' S dt C.J.e O S j ne ,
t_h e 1f)tt(UC IIS Oil w h ich - ~ 1S ceif'lco ue up O[)d
cco ccive down .
t-rl e ,n r'orrno \:.i Of) C11'iCl S1l.et;c h the po 1tj nom io I
3, l ) ~- 1 (ac ) ~ Li :,e 3 - lox
2
l,z l ( z. :;c, · 3 )
or 3
?C :; 2.
0 S
2
Fc:x.) isd ecreas1f)B of'\ c-~ : o_)_ ~__ c~ ; 31z) af\d ~C-x) ,s
o0 c31z ; ~) .