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Unformatted text preview: Chapter 6 1. Section 6.1 1. Below is a graph of a person’s annual earnings and annual money spent per year, over the course of their lifetime. Let I ( t ) denote annual earnings and S ( t ) denote annual money spent. Will this person need to find a financial advisor? dollars/year time in years I ( t ) S ( t ) Solution: The person’s savings at year t is precisely I ( t )- S ( t ). Notice that the number of years S ( t ) exceeds I ( t ) far outweighs the number of years the person saves money. Therefore, the person is in debt. From a more mathematical perspective, if we let N ( T ) denote the person’s networth after T years, it can be calculated as N ( T ) = Z T ( I ( t )- S ( t )) dt As you can see from the graph, most of the time I ( t )- S ( t ) < 0. 2. Below is the graph of a function f ( x ). Find the approximate locations of any inflection points and the locations of the absolute maximum and minimum for the antiderivative F ( x ). You may assume F (0) = 0. 1 2 3 4 5 1 2- 1- 2 f ( x ) 1 . 6 3 Solution: Notice that at about x = 2 and x = 3 . 5, the graph of f ( x ) flattens out. More specifically, at x = 2, f ( x ) goes from decreasing to increasing. Since F ( x ) = f ( x ), this is the same as saying that F ( x ) goes from decreasing to increasing. Thinking back to calculus 1, this means that the derivative of F ( x ), i.e. F 00 ( x ), goes from being negative to positive. Therefore,), goes from being negative to positive....
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This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.
- Summer '10