On a coordinate plane, a parabola opens up. It goes through (negative 3.25, 5), has a vertex of (1.7, negative 2.75), and goes t
hrough (6.25, 5). Solid circles appear on the parabola at (negative 3, 4), (0, negative 2), (1.5, negative 2.75), (3, negative 2), (6, 4).
Which is the rate of change for the interval between 3 and 6 on the x-axis?
–3
–2
2
3
Which is the rate of change for the interval between 3 and 6 on the x-axis?
–3
–2
2
3
1 answer:
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Parameterize the intersection by setting 
, so that
The length of the path
is then given by the line integral along ,
where
. We have
and so the line integral is
This result is fortuitous, since we can write
and so the integral reduces to
The length of the path
where
and so the line integral is
This result is fortuitous, since we can write
and so the integral reduces to