Calculus 1 Hour Exam 2 (continued) - Math 221 Fall, 2011

6.	The graph of a function y = f(x) and a point x1 are shown below. Using Newton’s method on f with initial approximation x1, mark on the x-axis where x2 will be and briefly explain how you found x2. One sentence should be enough.
7.	Gravel is being dumped from a conveyor belt at a rate of 30 ft^3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base, diameter, and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? Answer: 6 / 5π ft/min
8.	A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. after an hour the population has increased to 420 cells. Find an expression for the number of cells after t hours. Answer: y = 100 e ^(ln 4.2) t
9.	A graph of y = f(x) is given (not shown). a. On what intervals is f increasing and on what intervals is f decreasing? b. On what intervals is f concave up and on what intervals is f concave down? c. At what x-value does f have the largest rate of increase? Click here to continue with this exam.

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