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Mathematics
Mathematics
Problem
For
0
≤
x
≤
4
0\le x\le4
0
≤
x
≤
4
, let
f
(
x
)
=
x
3
−
6
x
2
+
9
x
f(x)=x^{3}-6x^{2}+9x
f
(
x
)
=
x
3
−
6
x
2
+
9
x
and define
A
(
t
)
=
∫
0
t
f
(
x
)
d
x
A(t)=\displaystyle\int_{0}^{t}f(x)\,dx
A
(
t
)
=
∫
0
t
f
(
x
)
d
x
. On which subintervals of
(
0
,
4
)
(0,4)
(
0
,
4
)
is
A
A
A
concave up?
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