Prove the hw7 that is "prove there is min" please follow the same above format which used in classwork HW7:Thm: If f: [a, b]→ R is continuous onthen 3 maximum M=max{f(x) | x e [a, b]}[a, b]3x, e [a,b] s.t f(x,)=MProof: O ¿f(x)|x ¢ [a,b]}O byhas an uperbound.boundedthmO sup { s6o)lx¢[a,67} =5 exists ©O Vje IN S-f G lim $(x;)=lim YnO step4+sandwichThmlimy =S%3Din the setOby steps 7-9(リ f()= maxWIf a sup isa set thennitis the max.f(x,)=maX QED.HW7] Prove thereis a min,

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Prove the hw7 that is "prove there is min" please follow the same above format which used in classwork

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Question

Prove the hw7 that is "prove there is min"

please follow the same above format which used in classwork

HW7:
Thm: If f: [a, b]→ R is continuous on
then 3 maximum M=max{f(x) | x e [a, b]}
[a, b]
3x, e [a,b] s.t f(x,)=M
Proof: O ¿f(x)|x ¢ [a,b]}
O by
has an uper
bound.
bounded
thm
O sup { s6o)lx¢[a,67} =5 exists ©
O Vje IN S-f<S is not @defn
classwork
bound of sup
an
"pper
O 3y; e {f)xE [a, b] } @ defn
S-fayjks
y=$(x;7 x;
"ppar
bóund
e [a,b] G defn
of our
set
OB-0
Thm
のf(x;,)→ fC)6 。
&lim f(x;)=lim
Timits
O by steps
step
+sandwich
Thm
4
lim y =S
kう。

G lim $(x;)=lim Yn
O step4
+sandwich
Thm
limy =S
%3D
in the set
Oby steps 7-9
(リ f()= max
WIf a sup is
a set thenn
it
is the max.
f(x,)=maX QED.
HW7] Prove there
is a min,

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