Apologies for the misunderstanding.

In most examples the car starts at full velocity. No time is spent picking up speed (the velocity is a "step function"). The distance often starts at zero; the car is considered new. Those decisions make the graphs as neat as possible, and it is the same in the example that was presented here.

The relation presented in such way needs algebra, not calculus. Therefore you are correct.

Calculus can be used by taking the derivative of the velocity equation with respect to time. This derivative is the equation for acceleration. Set the acceleration equation equal to zero and solve for time. More than one solution may exist, which is fine. Remember acceleration is the slope of the velocity equation and the derivative is just the slope of the original line. When the slope is equal to zero, the line is horizontal. This occurs at an extremum, i.e., a maximum or a minimum. Test each solution to determine whether it is a maximum or a minimum. Choose a point just to the left of the extremum and another point just to the right. If acceleration is negative to the left and positive to the right, the point is a minimum velocity. If acceleration is positive to the left and negative to the right, the point is a maximum velocity.

However, presenting the relation in this way still makes no use of the Rule de l'Hopital. Therefore you are correct.
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