One mile from a house, down a straight road, is an intersection. A highway
runs through the intersection, perpendicular to the road to the house.
Suppose an automobile travels 60 mph along the highway
- How fast is the distance between the car and the house increasing when the
car is 3 miles past the intersection?
- How fast is the distance between the car and the house increasing when the
car is x miles past the intersection?
- Confirm your answer to the previous part by substituting x = 3 and x = 0.
- Suppose the speed of the car x miles past the intersection is a function
s(x). (So previously, s(x) = 60 was a constant function.) Now
how fast is the distance between the car and the house increasing when the
car is x miles past the intersection?