Table of Contents
When can you apply the mean value theorem?
The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function’s average rate of change over [a,b].
When can the mean value theorem does not apply?
f(b) − f(a) b − a = f (c). Consider the function f(x) = |x| on [−1,1]. The Mean Value Theorem does not apply because the derivative is not defined at x = 0.
Does the mean value theorem apply to the second derivative?
In one variable calculus, the mean value theorem relates the first derivative of a function to the nearby values of the function. The analogue for second (and higher order) derivatives is known as ‘Taylor’s Theorem (with remainder)’. Here I state it only for second order derivatives.
How can police catch you speeding?
Police cars Officers spotting a speeding car might follow it, and using an in-car camera system, they are able to record your speed, then pull you over if you’ve exceeded the limit.
Does the Mean Value Theorem guarantee a value C?
The mean value theorem guarantees, for a function f that’s differentiable over an interval from a to b, that there exists a number c on that interval such that f ′ ( c ) f'(c) f′(c)f, prime, left parenthesis, c, right parenthesis is equal to the function’s average rate of change over the interval.
Does law enforcement use the mean value theorem to nab speeders?
However, law enforcement officials have used the mean value theorem to nab speeders. In 2005 Scotland began a system that used cameras to compute the average velocity of cars at locations along a 28-mile stretch of A77. They used this information to issue speeding tickets.
What does the mean value theorem say about the car?
Then and . Assuming is differentiable, the mean value theorem says that there is a such that In other words, at some time during the drive, the car was traveling 80 mph (the speed limit of the PA Turnpike is 65 mph).
How does a police officer determine a suspect’s speed?
With this technique, the officer must maintain a constant distance between the police vehicle and the suspect’s car long enough to make a reasonably accurate estimate of its speed. Some states have rules requiring the officer to verify speed by pacing over a certain distance.
Can E-Z passes be used to issue speeding tickets?
As an example, I gave them a hypothetical means of using E-Z Passes to issue speeding tickets. (An E-Z Pass is an electronic device in your car that reads when you pass through highway toll booths. It is tied to your credit card and is used to automatically collect tolls.)