MATH991

FirstDerivTestforlocalExtrema oddsolutions

Fox 2 2 3 7 domain all reals

f x 0

x 3 4 FILMI 34

fldne none

it t a localmin x 34 fl t b f increasing

3 4,0

fdecreasing 01 34

fix x4 4 3 2 domain all reals f x 4

3 12 2

044 3 0 fifth XO 2 3 F'done none

f

x g f g a localmin 8 3b f increasing 3,8 f t t t t fdecreasing

Go O V 0,3

fix x53 domain allreals grittingf x 36 5724 fldne none3 x 5 2 0

t

I I a no localextrema

b f increasing f t t t t to 5 V15

17 113 2 domain allreals agithumonef x 3 13 fldne XO

f a localmin x o

c f f I b f increasing o o

fdecreasing C 0,0 fl t t

t t t

fix X 3 2 45 5 domain all reals f x 3

2 6 45 GEMMA

sis31 42 15 D3xt x 3 o f'dne none

none x S x 3

I I localmax x 3 localmin x s f increasing 5,3

fl t t f decreasingC D 5 V13 D

fly x I t domain X 0 crit num

fly x2 fl 0 none fldne XO VA

a no localextrema

fi IT b fi'sdecreasingon

f I I f o O UCO a

fly xt 2 4 9 1 2 domain X 0

f 17 1 9 2

E FYI 1 87 3 3

fldne 7 0 VA

t

I g II go I a localmax x 3localMin x 3 f I I I I b

f increasing C 0 3 V63 8

f decreasing C3,0 UCO 3

text Ip

domain all reals crit

hum.fiO x 1 Ifly 1 I x2 XCX It M fidme noneItx42

É qt qt qta localmin

7 1 fl I I I local max

I b f increasing C1,1 decreasing to DUG o

fat 4 domain Xt 212

f x 2 62 4 x2 2x x247 f'done 7 212 VA

fitting

a localmax to t III Ifb f increasing CN 2 V62 0

I

f decreasing f I I It I O 2 V62 N

flx7 2 1 5 zx

domain x 53

gittnonefix 21537 ADG fidne x 53 VA5 3 72

a no localextremeIII f 4 to 7

f I I b f increasing C O O V 0,0

fix x 1743 domain all reals

f 17 31 1543 D gqftnmp F.br fldnex 1

f

y a localmin 4 1

I b f increasing 1,0 f I

t fdecreasing C D D t

230 fly ex 4x domain all reals flex 4 0 crithum

ex 4 tho x In4

x ln4 v1.4 fldne none

If y a localmin x ln4 b f increasing en4 o

fl f decreasing to ln4 CET Ex foxy pet É domain all reals

flex 2xegg ex aritham

FEO X 012 xoxo A MII

f'done none ex

fi

q

a localmax x2 localmin x 0

b f increasing 0,2 fl t t t

t I f decreasing

c o O V62 D

far Off exté domain all reals

fix Ilex éx ex Ex FILMY

FEI ext f'done none ex l or x Int O

fi s I g T y

a localmin Xo

b f increasing 0,0 f

I ft fdecreasing c 0,0

El El

fix Intf domain XO fix x Cnn I GITTE e

x2 fldne 7 0 VA

tenno I I T ITI In X EET f

p I 1 I f I Ina'te or e tenno Ito till a localmin x e

local max x e b