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Mathematics
Problem
Consider the function whose derivative is
k
′
(
x
)
=
(
x
+
2
)
2
/
3
(
x
−
5
)
x
−
1
,
−
3
≤
x
≤
6.
k'(x)=\frac{(x+2)^{2/3}(x-5)}{x-1},\qquad -3 \le x \le 6.
k
′
(
x
)
=
x
−
1
(
x
+
2
)
2/3
(
x
−
5
)
,
−
3
≤
x
≤
6.
On which of the following collections of open intervals is
k
k
k
increasing on the given domain? a)
(
−
3
,
1
)
∪
(
5
,
6
)
(-3,1)\cup(5,6)
(
−
3
,
1
)
∪
(
5
,
6
)
b)
(
−
2
,
1
)
∪
(
5
,
6
)
(-2,1)\cup(5,6)
(
−
2
,
1
)
∪
(
5
,
6
)
c)
(
−
3
,
−
2
)
∪
(
5
,
6
)
(-3,-2)\cup(5,6)
(
−
3
,
−
2
)
∪
(
5
,
6
)
d)
(
−
3
,
−
2
)
∪
(
1
,
5
)
(-3,-2)\cup(1,5)
(
−
3
,
−
2
)
∪
(
1
,
5
)
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