Velocity of a car The graph shows the position s=f(t) of a car t hours after 5:00 P.M. relative to its starting point s=0,where s is measured in miles. <IMAGE>
b. At approximately what time is the car traveling the fastest? The slowest?

Verified step by step guidance

1. To determine when the car is traveling the fastest or the slowest, we need to analyze the graph of the position function s = f(t). The speed of the car is given by the derivative of the position function, which is the velocity v(t) = f'(t).
2. Identify the points on the graph where the slope of the tangent line is the steepest. The steepest positive slope indicates the fastest speed in the forward direction, while the steepest negative slope indicates the fastest speed in the reverse direction.
3. Look for points on the graph where the slope of the tangent line is zero. These points correspond to the car traveling the slowest, as the velocity is zero at these points, indicating a momentary stop or change in direction.
4. Estimate the time intervals on the graph where the slope of the tangent line changes from positive to negative or vice versa. These intervals can help identify when the car transitions from speeding up to slowing down or vice versa.
5. Use the visual information from the graph to approximate the specific times when the car is traveling the fastest and the slowest, based on the steepness and direction of the slopes at various points.