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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
{
x
2
,
x
<
1
k
x
2
−
(
k
−
1
)
,
x
≥
1.
f(x)=\begin{cases}x^{2}, & x<1\\ kx^{2}-(k-1), & x\ge 1.\end{cases}
f
(
x
)
=
{
x
2
,
k
x
2
−
(
k
−
1
)
,
x
<
1
x
≥
1.
If
f
f
f
is differentiable at
x
=
1
x=1
x
=
1
, what is the value of
k
k
k
? a)
k
=
0
k=0
k
=
0
b)
k
=
1
k=1
k
=
1
c)
k
=
1
2
k=\dfrac{1}{2}
k
=
2
1
d) No such value of
k
k
k
exists
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