a 10 ft display sign is 10 feet off the ground. Find the distance from the sign of a point on the ground where the subtended angle of the sign is a maximum.
Let be the optimal distance from the sign, be the subtended angle of the sign and be the angle formed by the ground and the ray from the optimal viewpoint to the bottom of the sign. Then and . Using the formula for the tangent of difference, you can express through . Since is a monotonic function on , the maximum point of is also the maximum point of .