The position (in thousands of feet) of a car driving along a straight road at time \(t\) in minutes is given by the function \(y = s(t)\) that is pictured below.
Let \(v(t)\) denote the velocity of the car (in thousands of feet per minute) at time \(t\) (in minutes). Which graph A-F is the best representative of the derivative function \(v'(t)\)?
Which of the following statements are true? Select all that apply.
A. When \(v'(t)\) is negative, the car is slowing down.
B. When \(v'(t)\) is negative, the car is moving backwards.
C. The function \(v'\) represents the position of the car.
D. If \(v'(t)\) is zero, then \(v(t)\) must be zero.
E. When \(v(t)\) is positive, \(v'(t)\) must also be positive.
F. There are times when \(v'(t)\) is zero and \(v(t)\) is not zero.
G. The function \(v'\) represents the acceleration of the car.
H. None of the above statements are true.