Homework Soursestate patrol officer saw a car start from rest at a highway
state patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to another officer 30 mi along the highway. When the car reached the location of the second officer 26 min later, it was clocked going 60 mi/hr. The driver of the car was given a ticket for exceeding the 60/mi/hr speed limit. Why can the officer conclude that the drive exceeded the speed limit?
A? -the officer can conclude the drive exceeded the speed limit becuase by the extreme value theorem, at some time c, the car was travelling at a speed of ? miles per hour.
B? -the officer can conclude the drive exceeded the speed limit because, by Rolle\'s theorem, at some time c, the car was travelling at a speed of ? miles per hour.
C? -the officer can conclude the driver exceeded the speed limit because by the mean value theorem,at some time c, the car was travelling at a speed of ? miles per hour.
Answer rounded to 2 decimal places
A? -the officer can conclude the drive exceeded the speed limit becuase by the extreme value theorem, at some time c, the car was travelling at a speed of ? miles per hour.
B? -the officer can conclude the drive exceeded the speed limit because, by Rolle\'s theorem, at some time c, the car was travelling at a speed of ? miles per hour.
C? -the officer can conclude the driver exceeded the speed limit because by the mean value theorem,at some time c, the car was travelling at a speed of ? miles per hour.
Answer rounded to 2 decimal places
Solution
The answer is C Explanation: The mean value theorem states the following: If f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists some value x = c such that f\'(c) = [f(b) - f(a)]/[b-a] This implies the following in \"lay man\'s\" terms: the instantaneous speed (the speed at any given time) must be equal to his average speed Since the driver is driving along the highway, we can assume his position to be continuous and differentiable his average speed is defined as: average speed = [x(b) - x(a)]/[b-a] where x represents his position average speed = [30 - 0]/[.4333 - 0] = 69.23 mi/hr note .43333 hrs is 26 minutes Therefore, by the MVT the police officers can determine that at some point in time (even though he was only driving 60mph at the second patrol officer\'s location) since his average speed was approximately 69.23 mi/hr there was a point in time during the 26 minutes that his speed exceeded 60 mph. BOL
