Maximizing
the View
by
Gayle Gilbert & Greg Schmidt
A 4x4 picture hangs on the wall such that its bottom edge is 2 ft above eye level. How far back from the picture should you stand, directly in front of the picture, in order to view the picture under the maximum angle?
We need to find the value of 
, which will maximize 
.
We first note that using basic trigonometric properties we have that
.
Similarly, 
And so,
Now by substitution for 
we have that
We will continue by differentiating 
and setting it
equal to 
as to find the
value of 
, which makes it maximal.
So we have
.
So we have that 
. Now, as far as
we are concerned distance is positive value and so we take 
We also now know the maximal angle under which we can view the picture.
