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Mathematics
Problem
For the function
f
(
x
)
=
∣
x
∣
f(x)=|x|
f
(
x
)
=
∣
x
∣
, what are the values of the one-sided derivatives at
x
=
0
x=0
x
=
0
? a)
L
f
′
(
0
)
=
1
,
R
f
′
(
0
)
=
1
L f'(0) = 1,\; R f'(0) = 1
L
f
′
(
0
)
=
1
,
R
f
′
(
0
)
=
1
b)
L
f
′
(
0
)
=
0
,
R
f
′
(
0
)
=
0
L f'(0) = 0,\; R f'(0) = 0
L
f
′
(
0
)
=
0
,
R
f
′
(
0
)
=
0
c)
L
f
′
(
0
)
=
−
1
,
R
f
′
(
0
)
=
1
L f'(0) = -1,\; R f'(0) = 1
L
f
′
(
0
)
=
−
1
,
R
f
′
(
0
)
=
1
d)
L
f
′
(
0
)
=
1
,
R
f
′
(
0
)
=
−
1
L f'(0) = 1,\; R f'(0) = -1
L
f
′
(
0
)
=
1
,
R
f
′
(
0
)
=
−
1
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