What is the maximum value of f(x)=3x2−x3?
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Answers
Answered by
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the max value will therefore be as
x
→
−
∞
then
y
→
∞
.
Explanation:
the dominant term in this function is the
−
x
3
term.
so for large negative x, the function is effectively
f
(
−
x
)
=
−
(
−
x
)
3
=
x
3
. the max value will therefore be as
x
→
−
∞
then
y
→
∞
.
equally for large positive x, the function is effectively
f
(
x
)
=
−
(
x
)
3
=
−
x
3
. the min value will therefore be as
x
→
+
∞
then
y
→
−
∞
.
maybe you are using calculus, in which case you might also be expected to look at:
f
'
(
x
)
=
6
x
−
3
x
2
=
x
(
6
−
3
x
)
that will be zero at critical points so
x
(
6
−
3
x
)
=
0
⇒
x
=
0
,
x
=
2
with
f
(
0
)
=
0
,
f
(
2
)
=
4
. but these are local min and max.
you can use
f
'
'
(
x
)
=
6
−
6
x
to verify the nature of these turning points if that is needed eg if i have misunderstood the question.
f
'
'
(
0
)
=
6
[
min
]
,
f
'
'
(
2
)
=
−
6
[
max
]
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