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Mathematics
Mathematics
Problem
Consider the piecewise function
f
(
x
)
=
{
(
x
+
2
)
2
/
3
,
x
≤
0
x
2
,
x
>
0
.
f(x)=\begin{cases}(x+2)^{2/3},&x\le 0\\x^{2},&x>0\end{cases}.
f
(
x
)
=
{
(
x
+
2
)
2/3
,
x
2
,
x
≤
0
x
>
0
.
For which of the following
x
x
x
-values does
f
′
(
x
)
f'(x)
f
′
(
x
)
fail to exist? a)
x
=
−
2
only
x=-2\text{ only}
x
=
−
2
only
b)
x
=
0
only
x=0\text{ only}
x
=
0
only
c)
x
=
−
2
and
x
=
0
x=-2\text{ and }x=0
x
=
−
2
and
x
=
0
d)
x
=
−
2
and
x
=
2
x=-2\text{ and }x=2
x
=
−
2
and
x
=
2
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