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Mathematics
Problem
Suppose
f
f
f
is differentiable and
f
′
(
2
)
<
0
f'(2)<0
f
′
(
2
)
<
0
. Let
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
F(x)=\displaystyle\int_{0}^{x} f(t)\,dt
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
. Determine whether the graph of
F
F
F
is concave up or concave down at
x
=
2
x=2
x
=
2
.
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