If you feel lost at this point you may want to see the first part of this solution, or you may want to go back to the original problem.
If you will recall, the formula for our angle is
y = arctan ((4-x)/3) + arctan (x/3)
Which has the following graph:
To find that maximum point, we must defferentiate our equation, set it equal to zero and solve it:
y' = -1/(1+((4-x)/3)^2) + 1/(1+(x/3)^2)
= -9/(9+(4-x)^2) + 9/(9+x^2)
At this point, combine fractions and simplify to get:
y' = [9(16-8x)]/[(4-x)^2*(9+x^2)]
To solve this for zero all we need is to set the numerator equal to zero:
9(16-8x) = 0
and your solution is x = 2
The angle at this point is about 67.38 degrees.
If your eye level is at 2 ft above the bottom of a 4ft picture, that means you will get the best angle if you look straight at the picture.
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