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Mathematics
Problem
Let
f
(
x
)
=
k
x
4
f(x) = kx^4
f
(
x
)
=
k
x
4
. The point
P
(
1
,
k
)
P(1, k)
P
(
1
,
k
)
lies on the curve of
f
f
f
. At
P
P
P
, the normal to the curve is parallel to
y
=
−
1
8
x
y = -\frac{1}{8}x
y
=
−
8
1
x
. Find the value of
k
k
k
.
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