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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 velocity 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

AI only
BII only
CIII only
DEither I or III
EEither II or III

Verified Answer :

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

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