When is the rate of separation between the ends of the hour and minute hands of a clock at a maximum?
Clicking the Play button will set the clock in motion and trace out a graph of the distance between the ends of the clock hands and the derivative of that curve.
You will likely need to increase the vertical scale of the graph to locate the maximum point.
The refresh button will return the applet to its initial state.

The length of the minute hand can be adjusted by dragging the ml slider.
The ratio of the lengths of the minute and hour hands can be adjusted using the mlhlRatio slider.
Time, in minutes after 12:00, can be set by dragging the t slider.
The derivative curve is actually a plot of the slope of a secant to the first curve. The secant is constructed by drawing a line through 2 points on the separation curve with a time difference of deltat. You can drag the deltat slider to change the time separation between the two points and bring the secant closer to being a tangent.

Is the time of maximum effected by the length of the minute hand?

Is the time of maximum effected by the ratio of the lengths of the minute and hour hands?

Is the time (minutes after the hour) of maximum the same for each hour?