You are standing in the Uffizzi gallery admiring a painting by Botticelli. The painting is huge, and your
viewing location is pictured below; all measurements are in meters.
(a) If
x
is the your distance from the wall holding the painting, find a function
A(x)
that computes the
angle
a
in the picture;
A(x)=
$$
arctan
(13
x
)−
arctan
(3
x
)
(b) Find the rate of change with respect to
x
of the angle
a
when you are at the location
$$11+(13
x

(c) Find the rate of change with respect to
x
of the angle
a
when you are at the location
$$11+(134)2·(−1316)−11+(34)2·(−316)
m. (Exact answer.)
(d) Find the rate of change with respect to
x
of the angle
a
when you are at the location
x=13
x=4

m. (Exact answer.)
(e) Find the location where the rate of change with respect to
x
of the angle
a
is zero
$$√39
m.(Exact answer.)
(f) When you are standing at the location to maximize
a
, what is the value of
a
?

(Radians to three decimal places.)
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