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Mathematics
Mathematics
Problem
Let
h
(
x
)
=
{
k
x
+
1
,
x
≤
2
,
x
2
−
3
,
x
>
2.
h(x)=\begin{cases} kx+1,& x\le 2,\\ x^{2}-3,& x>2. \end{cases}
h
(
x
)
=
{
k
x
+
1
,
x
2
−
3
,
x
≤
2
,
x
>
2.
Determine the value of
k
k
k
that makes
h
h
h
continuous at
x
=
2
x=2
x
=
2
so that the Intermediate Value Theorem applies on the interval
[
0
,
3
]
[0,3]
[
0
,
3
]
.
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