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Mathematics
Mathematics
Problem
Define the function
h
(
x
)
=
{
x
2
−
4
x
−
2
,
x
≠
2
,
k
,
x
=
2.
h(x)=\begin{cases}\dfrac{x^{2}-4}{x-2}, & x\neq 2,\\k, & x=2.\end{cases}
h
(
x
)
=
⎩
⎨
⎧
x
−
2
x
2
−
4
,
k
,
x
=
2
,
x
=
2.
For which value of
k
k
k
does
h
′
(
2
)
h'(2)
h
′
(
2
)
exist? a)
k
=
1
k=1
k
=
1
b)
k
=
4
k=4
k
=
4
c)
k
=
2
k=2
k
=
2
d) No value of
k
k
k
makes
h
′
(
2
)
h'(2)
h
′
(
2
)
exist
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