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Mathematics
Problem
Let
f
(
x
)
=
x
3
−
3
x
2
+
k
f(x)=x^{3}-3x^{2}+k
f
(
x
)
=
x
3
−
3
x
2
+
k
on the closed interval
[
0
,
2
]
[0,2]
[
0
,
2
]
. The function is strictly increasing on
[
0
,
2
]
[0,2]
[
0
,
2
]
if a)
k
>
3
k>3
k
>
3
b)
k
=
3
k=3
k
=
3
c) No real value of
k
k
k
makes
f
f
f
strictly increasing on
[
0
,
2
]
[0,2]
[
0
,
2
]
d)
k
<
3
k<3
k
<
3
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