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Mathematics
Mathematics
Problem
Determine the value of
a
a
a
such that the piecewise function
k
(
x
)
=
{
(
x
−
5
)
2
,
x
≤
5
,
a
(
x
−
5
)
+
25
,
x
>
5
k(x)= \begin{cases} (x-5)^{2}, & x\le 5,\\ a(x-5)+25, & x>5 \end{cases}
k
(
x
)
=
{
(
x
−
5
)
2
,
a
(
x
−
5
)
+
25
,
x
≤
5
,
x
>
5
is differentiable at
x
=
5
x=5
x
=
5
.
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