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# Critical Numbers, Derivatives and Rates of Change

See the attached file.
The function has one critical number. Find it.

A student decided to depart from Earth after his graduation to find work on Mars. Before building a shuttle, he conducted careful calculations. A model for the velocity of the shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisoned at t = 60.7 s, is given by

(in feet per second). Using this model, estimate
the absolute maximum value
and absolute minimum value
of the ACCELERATION of the shuttle between liftoff and the jettisoning of the boosters.

Water is leaking out of an inverted conical tank at a rate of cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height meters and the diameter at the top is meters. If the water level is rising at a rate of centimeters per minute when the height of the water is meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Note: Let "R" be the unknown rate at which water is being pumped in. Then you know that if is volume of water, . Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by?

#### Solution Summary

Critical numbers, derivatives and rates of change are investigated and discussed in the solution. The solution is detailed and well presented.

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