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Mathematics
Mathematics
Problem
A differentiable function
p
p
p
satisfies
p
′
(
x
)
=
k
e
2
x
+
4
p'(x)=k e^{2x}+4
p
′
(
x
)
=
k
e
2
x
+
4
for all real
x
x
x
, where
k
k
k
is a constant. If
p
(
0
)
=
5
p(0)=5
p
(
0
)
=
5
and
p
(
1
)
=
20
p(1)=20
p
(
1
)
=
20
, find the value of
k
k
k
.
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