The total stopping distance T of a vehicle is shown below, where T is in feet and x is the speed in miles per hour. T = 2.5x + 0.5x2 Approximate the change and percent change in total stopping distance as speed changes from x = 17 to x = 19 miles per hour. Step 1 As speed changes from x = 17 to x = 19 miles per hour, an approximation of the change in x is Ax dx=19 19-17 2 B Step 2 To approximate the change in total stopping distance, differentiate T = 2.5x +0.5x2 with respect to x and solve for the differential dT. Step 3 dT 2.5 dx 2.5+ (1)x dx 2.5+ dT (2.5+1(x) Substitute 17 for x and 2 for dx, to conclude that the approximate change in total stopping distance is as follows. dT = (2.5+ X ft