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Curve study/e^(-2x)-2e^(-x)/x not negative/Morse potential/Exercise
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Discuss the behavior of the function graph of
f
:
R
⟶
R
,
x
⟼
f
(
x
)
=
e
−
2
x
−
2
e
−
x
.
{\displaystyle f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto f(x)=e^{-2x}-2e^{-x}.}
Determine especially the monotonicity behavior, the extrema of
f
{\displaystyle {}f}
,
lim
x
→
∞
f
(
x
)
{\displaystyle {}\operatorname {lim} _{x\rightarrow \infty }\,f(x)}
and also for the derivative
f
′
{\displaystyle {}f'}
.
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