Section 4.6 - The Mean Value Theorem 1. Explain the difference between Rolle's Theorem and The Mean Value Theorem. 2. The population of a culture of cells grows according to the function P(t) = 100t t+1' , where t 2 0 is measured in weeks. (a) What is the average rate of change in the population over the interval [0, 8]? (b) At what point in the interval [0, 8] is the instantaneous rate of change equal to the average rate of change? 3. A state patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to another officer 30 miles along the highway. When the car reached the location of the second officer 30 minutes later, it was clocked going 60 mi/hr. Can the patrol officer conclude that the driver exceeded the 60 mi/hr speed limit? Explain