A big clock has a minute hand 3 ft long and a second hand 4 ft long. let x be the distance between their tips. find max value of (dx)/(dt) *d for derivative

Answer 1

According to the law of cosines, the distance between the tips is given by
D^2 = a^2 + b^2 - 2 ab cos theta
where theta is the angle bewteen the hands, and a and b are the lengths of the hands. In this case, a = 4 and b = 3

D^2 = 25 - 24 cos theta
The rate of change of D is given by
2D dD/dt = 24 sin theta* d(theta)/dt

Note that D is also a function of theta. The maximum dD/dt occurs where sin theta/D is a maximum.

d(theta)/dt = 2 pi (1/60 - 1/720) radians/minute

Answer 2

My d(theta)/dt is wrong. I calculated if for the minute and hour hand. For the second and minute hand, it is
d(theta)/dt = 2 pi (1/60 - 1/3600) radians/second. You are still left with the chore of finding when (1/D) sin theta is a maximum.