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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
{
x
2
,
x
≤
1
,
k
x
2
,
x
>
1.
f(x)=\begin{cases}x^{2}, & x\le 1,\\ kx^{2}, & x>1.\end{cases}
f
(
x
)
=
{
x
2
,
k
x
2
,
x
≤
1
,
x
>
1.
Determine the value of
k
k
k
that makes
f
f
f
differentiable at
x
=
1
x=1
x
=
1
.
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