Suppose an object moves along the y-axis so that its location is y = f(x)= x² + x at time x (y is in meters and x is in seconds). Find the average veloity for x changing from 3to 3 + h seconds.
A) 7-h m/s
B) 12+h m/s
C) 12-h m/s
D) 7 +h m/s

Question

Suppose an object moves along the y-axis so that its location is y = f(x)= x² + x at time x (y is in meters and x is in seconds). Find the average veloity for x changing from 3to 3 + h seconds.
A) 7-h m/s 
B) 12+h m/s 
C) 12-h m/s 
D) 7 +h m/s

Quizplus · Accepted Answer

The average velocity is given by the change in position over the change in time. For x changing from 3 to 3 + h, the average velocity is [f(3 + h) - f(3)] / h. Calculating f(3) = 3² + 3 = 12 and f(3 + h) = (3 + h)² + (3 + h) = 9 + 6h + h² + 3 + h = 12 + 7h + h². The change in position is (12 + 7h + h²) - 12 = 7h + h². Dividing by h gives (7h + h²)/h = 7 + h. Thus, the average velocity is 7 + h m/s.

Suppose an Object Moves Along the Y-Axis So That Its