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Mathematics
Problem
Let
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
where
f
f
f
is differentiable on
R
\mathbb R
R
. Describe how the sign of
f
(
t
)
f(t)
f
(
t
)
affects whether
A
(
t
)
A(t)
A
(
t
)
is increasing or decreasing at that same value of
t
t
t
.
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