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Zig zag/Continuity/Differentiability/Extrema/Exercise
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Consider the function
f
:
R
⟶
R
,
{\displaystyle f\colon \mathbb {R} \longrightarrow \mathbb {R} ,}
defined by
f
(
x
)
=
{
x
−
⌊
x
⌋
,
if
⌊
x
⌋
is even
,
⌊
x
⌋
−
x
+
1
,
if
⌊
x
⌋
is odd
.
{\displaystyle {}f(x)={\begin{cases}x-\lfloor x\rfloor ,{\text{ if }}\lfloor x\rfloor {\text{ is even}},\\\lfloor x\rfloor -x+1,{\text{ if }}\lfloor x\rfloor {\text{ is odd}}\,.\end{cases}}\,}
Examine
f
{\displaystyle {}f}
in terms of continuity, differentiability and extremes.
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