A car's odometer (mileage counter) reads exactly 59,024 miles at 8:00am and 59,094 miles at 10:00am. Assuming the car's position and velocity functions are differentiable, what theorem can be used to show that the car was traveling at exactly 35mph at some time between 8:00am and 10:00am?

a) Intermediate Value Theorem for Derivatives

b) Extreme Value Theorem

c) Mean Value Theorem