The mean value theorem states that if F(x) is a differentiable function on the interval [a,b], then there exists some number c between a and b such that the following formula is true. Use this to explain why the mean value theorem implies that if a car averages 67 miles per hour in some 10-minute interval, then the car's instantaneous velocity is 67 miles per hour at least once in that interval. F(b)-F(a) F'(c)= b-a Choose the correct answer below. OA. The car's speed of 67 miles per hour is defined as the average rate of change of the car at point c, making the function continuous. Since the function is continuous, it has a derivative at every point. Thus, the mean value theorem can be applied. OB. The car's time of 10 miles per hour is defined as the average rate of change of the car at point c, or f(c). Since the car drives continuously at an average speed of 67 miles per hour, the function is continuous. Thus, the mean value theorem can be applied. OC. The car's speed of 67 miles per hour is defined as the average rate of change of the car at point c, or f(c). Since car drives continuously over a 10-minute interval, or [0,10], the function is continuous. Thus, the mean value theorem can be applied. OD. The car's time of 10 miles per hour is defined as the average rate of change of the car at point c, making the function continuous. Since the function is continuous, it has a derivative at every point. Thus, the mean value theorem can be applied.