How do we know -5 is the absolute min here? Is it because we are decreasing from -infinity until we get to -5 then it goes to +infinity?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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How do we know -5 is the absolute min here? Is it because we are decreasing from -infinity until we get to -5 then it goes to +infinity?

2)
fx):-5c
ーXる
(-00,00)
f'(x)= 5e-x²
.2x
= loxe **
O = -
10xe*
set =0
x-0(critical point)
-plug back into flx)
X-0, f(x) = -5
Anything finite
divided by 00 = 0
メ=ロ,
-lowest
%3D
check
endpoints
lim -5e
-5
-5
verylarge
%3D
limit, never actually
goes to o
lim
-5e
-5
-5
verylarge
Absolute mnof -5 at X=0
no absolute max
Funcrionn ehnarges concavires
Transcribed Image Text:2) fx):-5c ーXる (-00,00) f'(x)= 5e-x² .2x = loxe ** O = - 10xe* set =0 x-0(critical point) -plug back into flx) X-0, f(x) = -5 Anything finite divided by 00 = 0 メ=ロ, -lowest %3D check endpoints lim -5e -5 -5 verylarge %3D limit, never actually goes to o lim -5e -5 -5 verylarge Absolute mnof -5 at X=0 no absolute max Funcrionn ehnarges concavires
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