Math 1A: introduction to functions and calculus Oliver Knill, 2011Lecture 35: WorksheetCalculus in EconomicsThe fact that extremisation is a big deal in economics is already inthe word. We look at more examples. Assume we have a couple ofdata points and we want to find the best line y = mx through thisin the sense that the sum of the squares of the points to the line isminimal. This lea ds to an extre ma l problem which is a special ca se ofa data fitting problem. It would be more adequate to fit with linesy = mx + b or more generally with functions but then we have morevariables and run into multivariable ca lculus or linear algebraproblems much outside the scope of this course. But if we have onlyone pa rameter, we get a single variable calculus problem.1 Find the best line y = mx through the points (1, 1), (3, 2), (2, 5).We have to minimize the function.f(m) = (m − 1)2+ (3m − 2)2+ (2m − 5)2Find the minimum. Solution. 17/1 4Lets take a different set of data points a nd look at the problem tofit functions of the form y = x + b.2 Find the best line y = x+b through the points (1, 2), (2, 5), (−1, 2), (4Source: ”Dominik Heckner and Tobias Kretschmer: Don’t worryabout Micro, 2008 ”, pages
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