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.

** **