An airplane traveling toward Denver is 642 miles away ay 1:30pm and 42 miles away at 3:00pm. Assuming the plane's position and v
elocity functions are differentiable, which of the following can be used to show that the plane was traveling at exactly 400 mph at some time between 1:30pm and 3:00pm? I. Extreme Value Theorem
II. Mean Value Theorem
III. Intermediate Value Theorem for Derivatives
A) I only
B) II only
C) III only
D) Either I or III
E) Either II or III
The Mean Value Theorem is one of the most important theoretical tools in Calculus. It states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c) = ( f(b) - f(a) ) / b - a= 642 - 42 / 1.5 h= 400 mphso the answer B
