math101

SecondDerivativetestforlocalExtrema Oddsolutions

fly 2 2 3 7 domain allreals

F x 430 f 34 4 U x D

ÉÉÉÉÉn froocalmin x 314

flx7 tx3 2 2 Sx 10 domain all reals flex 4 5 FIX gÉo i f x 2 4 21207 fldne none

s t V f l d t N f haslocalmin 454 localmax

x I

Fox 3 5 5 3

F x 15 4 15 2 may

domain allreals

Ea.ir f x 60 3 307 300242 1 fidne none f 1 t t t CD I

Df o O testfails seebelow

qt g

has'ocalmax

localmin 1

wedonotneedtotestadditional values wehaveinfofromandduntest

fCx7 x 5 domain allreals

f x 46530 gifts f s O f x try fidne none goto stderintest

f

XIs fhas a localmin es f t t t

Fox Ig x 95 F47 1 2 95212721g

gÉI fldne none

f x Et Fx Zeta 2x Immer 2129 1 2

2

67974

24 F lo t

I n

f has a localmax x 0

fluffy domain allreals

F'txt 14th X W ÉÉÉÉgg HX Itt

x ta 7 1 x2 211 36 2 142370I x2 Mimed 2 4 2 1 24 23 1 2 2

2 2 23

f 4 t I N

f'll D I V

f has a localmax x 1 and a localmin x I