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Mathematics
Mathematics
Problem
Define
f
(
x
)
=
{
x
2
,
x
≤
1
,
k
x
+
(
1
−
k
)
,
x
>
1.
f(x)=\begin{cases} x^{2}, & x\le 1,\\ kx+(1-k), & x>1. \end{cases}
f
(
x
)
=
{
x
2
,
k
x
+
(
1
−
k
)
,
x
≤
1
,
x
>
1.
Find the value of
k
k
k
that ensures
f
f
f
is both continuous and differentiable at
x
=
1
x=1
x
=
1
.
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