Lesson 26: Optimization II: Data Fitting
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This document contains: 1) An announcement about an assigned problem set due November 28th and office hours. 2) A summary of the regression theorem for finding local maxima, minima, and saddle points of functions with two variables. 3) An example of classifying critical points of a function. 4) A discussion of finding the line of best fit to a set of data points by minimizing the sum of squared errors between the data points and fitted line.
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NOTE: the final location is section specific. Section 1 (morning) is in SILV 703, Section 11 (afternoon) is in CANT 200
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.
x
What can you say about g? 2 4 6 8 10f
The First Fundamental Theorem of Calculus
Theorem (First Fundamental Theorem of Calculus)
Let f be a con nuous func on on [a, b]. Define the func on F on [a, b] by
∫ x
F(x) = f(t) dt
a
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F′(x
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1) A checklist for graphing a function which involves finding where the function is positive/negative/zero, its monotonicity from the first derivative, and concavity from the second derivative.
2) An example of graphing the cubic function f(x) = 2x^3 - 3x^2 - 12x through analyzing its derivatives.
3) Explanations of the increasing/decreasing test and concavity test to determine monotonicity and concavity from a function's derivatives.
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