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Mathematics
Problem
Let
g
(
x
)
=
∫
3
h
(
x
)
f
(
t
)
d
t
g(x)=\displaystyle \int_{3}^{h(x)} f(t)\,dt
g
(
x
)
=
∫
3
h
(
x
)
f
(
t
)
d
t
, where
f
f
f
is continuous and
h
h
h
is differentiable. Explain in one or two sentences how the signs of
f
(
h
(
x
0
)
)
f\bigl(h(x_0)\bigr)
f
(
h
(
x
0
)
)
and
h
′
(
x
0
)
h'(x_0)
h
′
(
x
0
)
together determine whether
g
g
g
is increasing or decreasing at
x
=
x
0
x=x_0
x
=
x
0
.
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