Textbook Problem
Water is flowing at a constant rate into a spherical tank. Let V
be the volume of water in the tank and H( t) be the height of the
water in the tank at time t.
(a) What are the meanings of V' (t) and H (1)? Are these derivatives
positive, negative, or zero?
(b) 13 V" (1) positive, negative, or zero? Explain.
(c) Letti ty, and t, be the times when the tank is one-quarter full,
half full, and three-quarters full, respectively.
Are the values H"(t), H"(ty), and H"(ty) positive, negative, or zero?
Why?