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Mathematics
Problem
Let
f
f
f
be the piecewise-defined function
f
(
x
)
=
{
x
2
+
4
x
+
3
,
x
≤
−
1
2
−
x
,
x
>
−
1
f(x)=\begin{cases}x^{2}+4x+3, & x\le -1\\2 - x, & x> -1\end{cases}
f
(
x
)
=
{
x
2
+
4
x
+
3
,
2
−
x
,
x
≤
−
1
x
>
−
1
Determine whether
f
f
f
has a local extremum at
x
=
−
1
x = -1
x
=
−
1
and, if so, classify it.
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