HW-4.1 For each of the following, use the 5-step procedure on slide 5 to solve it and label each step. 1. (30 points) Two cars start from the same point. One travels south at 60 mph and the other travels west at 25 mph. At what rate is the distance between the cars increasing two hours later? Step 1: Draw a picture and use letters or symbols to label all those quantities which are changing. Step 2: Express symbolically the rates which are given or asked. Step 3: Write an equation without any derivatives and involving only those variables whose rates are given or asked. You may have to express some variables in terms of other. Step 4: Differentiate both sides of the equation found in Step 3 w.r.t. an appropriate variable using Implicit Differentiation. Solve for the rate that's asked and substitute the constant rates. Step 5: Re-draw the picture labeling the values of the variables and the rates at the given instant. Substitute these in the Step 4 equation to find the rate in question at the given instant.