1) When Mr. Brown, owner of a hardware store, arrived at work Saturday morning, he immediately called the police. The famous outdoor statue of Venus that graced his storefront had been damaged in what appears to have been a drive-by paintball shooting. The police detective on the case reviewed the footage (both audio and video) from the surveillance camera of the convenience store on the opposite side of the road. The function f(t) = t3 + 1.75 t2 models the path of the road and the vandalized statue stands at the point (4, 7.5). From the footage, the detective has determined that a loud thud occurred sometime during the t=3 and t=4 time frames. During that time frame, three vehicles (one at t=3, one at t=3.3, and one at t=3.4) passed by the curve in the road in front of the statue. From which vehicle was the paintball gun fired? Use calculus to determine which of the three vehicles was involved in the vandalism incident. Assume the paintball gun was aimed in the same direction that the vehicle was traveling. How confident are you in your answer? Could your solution method hold up in a court of law? Hint #1: Graph the function f(t). Mark the locations of the statue and the three passing vehicles. Hint #2: Draw the tangent line associated with each vehicle's location.

2) suppose that the vandals actually had a more powerful paintball gun and shot from farther back on the road, somewhere between t=0 and t=3, before even reaching the curve by the shop. Assuming they still had the paintball gun aimed in the vehicle's direction of travel, approximately where in this area was the vehicle when the shot was taken?