The depth of water in a certain nonuniform container is y = .025 t⁴ + -2.7 t² + 52, where depth y is in cm when clock time t is in seconds.

• At what average rate is the depth of water changing between clock times t = 14.6 and t = 14.7 seconds?
• At what average rate is the depth of water changing between clock times t = 14.6 and t = 14.61 seconds?
• At what average rate is the depth of water changing between clock times t = 14.6 and t = 14.601 seconds? 
• What do you estimate is the rate at which water depth is changing at clock time t = 14.6 seconds?

The rate at which water flows from a certain nonuniform cylinder is given by rate = .025 t³ + -2.7 t cm³ per minute, where t is in minutes.  How much do water do you think will flow between clock times t = 14.7 minutes and t = 29.2 minutes?