(3) Cyclists A and B rode along a straight one way road starting from the same location and they rode for one hour. Cyclist A rode half the time at a speed of 10 miles/ hour and the other half time at a speed of 30 miles / hour. Cyclist B rode half the total distance at a speed of 10 rniles/ hour and half the distance at a speed of 30/ hours. (a) Calculate the total distance traveled by cyclist A. Graph the velocity function for cyclist A and calculate the average trip velocity for cyclist A. (b) Calculate the total distance traveled by cyclist B. Calculate the average velocity for cyclist B. Graph the velocity function for cyclist B. (4) Use the limit denition of the rate of change to calculate how quickly f (a) : 3:2 changes at a: : 4. Solution. m = lim f\") _ \"4) = lim 52 _ (_4)2 b>4 b (4) b>4 b (4) _ b>4 _8' | ET /_'~ 0" | as v | | (5) Go to a nancial website pick your favorite stock. By p(t) denote the price at which the stock was exchanged at time t where t is measured in seconds from last Friday midday. What does 39(0) mean? What does p(7200) mean? Estimate the average rate of change of the stock for the following time intervals time interval [0,7200] [0,3600] [0,360] ] [0,180] [0,60]] average rate of change Based on your calculations do you think the instantaneous rate of change of the price p(t) exist? Can you briey describe in words the behavior of p(t) near t : O