(note that the angular velocity of the minute hand is 2*π*/(60×60) radians per second). Differentiate:

Set to to 0:

This equation can’t be solved analytically; using Wolfram|Alpha, I get *t* ≈ 493 seconds = 8 minutes 13 seconds, i.e. the insect is at its highest position at 12:08:13.

Check that d²*h*/d*t*² < 0 so that this is indeed a maximum value.