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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
(
x
−
2
)
(
x
−
5
)
f(x)=(x-2)(x-5)
f
(
x
)
=
(
x
−
2
)
(
x
−
5
)
for
0
≤
x
≤
7
0\le x\le7
0
≤
x
≤
7
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
. At what value of
t
t
t
in the interval
0
<
t
<
7
0<t<7
0
<
t
<
7
does
A
(
t
)
A(t)
A
(
t
)
attain its minimum?
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