152 HW6-w20.pdf - Math 15200 Homework 6 Due Wednesday...

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Math 15200: Homework 6 Due Wednesday, February 19 The following three problems will be graded out of a possible five points each. 1. Let f ( x ) = e - 2 x 2 (a) On which intervals is f increasing? Decreasing? (b) On which intervals is f concave up? Concave down? (c) Use the information in parts (a) and (b) to sketch the graph of f ( x ). Be sure to label all asymptotes, x - and y -intercepts, as well as the coordinates of any local max/min values and any inflection points. (d) Suppose that the area bounded by the graph of f ( x ), the x -axis, and the lines x = 0 and x = 1 is revolved around the y -axis. What is the volume of the resulting solid?

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