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Mathematics
Problem
A balloon’s height above the ground is modeled by a differentiable function
h
(
t
)
h(t)
h
(
t
)
, where
t
t
t
is measured in minutes. Suppose •
h
′
(
t
)
>
0
h'(t)>0
h
′
(
t
)
>
0
for
0
<
t
<
12
0<t<12
0
<
t
<
12
, •
h
′
(
12
)
=
0
h'(12)=0
h
′
(
12
)
=
0
, and •
h
′
(
t
)
<
0
h'(t)<0
h
′
(
t
)
<
0
for
t
>
12
t>12
t
>
12
. Explain what happens to the balloon at
t
=
12
t=12
t
=
12
minutes and why.
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