Question: The function y = 4 -(x 2 /4) on the interval [0, 4] is revolved about the line y = b (see figure). (a) Find

The function y = 4 -(x2/4) on the interval [0, 4] is revolved about the line y = b (see figure).


- 1 4 -2 y y = b 3 4 X


(a) Find the volume of the resulting solid as a function of b.


(b) Use a graphing utility to graph the function in part (a), and use the graph to approximate the value of b that minimizes the volume of the solid.


(c) Use calculus to find the value of b that minimizes the volume of the solid, and compare the result with the answer to part (b).

- 1 4 -2 y y = b 3 4 X

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