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Mathematics
Mathematics
Problem
A function
f
f
f
is defined by
f
(
x
)
=
{
x
2
+
2
x
x
,
x
<
0
,
x
2
+
1
x
2
+
5
,
x
≥
0.
f(x)= \begin{cases} \dfrac{x^{2}+2x}{x}, & x<0,\\ \dfrac{x^{2}+1}{x^{2}+5}, & x\ge 0. \end{cases}
f
(
x
)
=
⎩
⎨
⎧
x
x
2
+
2
x
,
x
2
+
5
x
2
+
1
,
x
<
0
,
x
≥
0.
Compute the exact values of
f
′
(
−
2
)
f'(-2)
f
′
(
−
2
)
and
f
′
(
1
)
f'(1)
f
′
(
1
)
.
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