Water is flowing at a constant rate into a spherical tank. Let V (t) 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’ (t)? Are these derivatives positive, negative, or zero?
(b) Is V” (t) positive, negative, or zero? Explain.
(c) Let t1, t2, and t3 be the times when the tank is one-quarter full, half full, and three-quarters full, respectively. Are the values H” (t1), H” (t2), and H” (t3) positive, negative, or zero? Why?