~~META:title=Chapter 3~~ ~~NOTOC~~ \\ ===== Critical Points and the Closed Interval Method ===== {{youtube>5ooKqwH3gvs}} {{youtube>qIilPJYGwg4}} \\ //Section 3.1 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ * Graphical understanding of extrema.\\ * Fermat's Theorem.\\ * Local extrema are critical points, the opposite isn't necessarily true.\\ * Extreme Value Theorem.\\ * The Closed Interval Method. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.1_critical_points.pdf|Classroom Slides PDF]] \\ ===== The Mean Value Theorem ===== //Section 3.2 in Stewart's Calculus.// [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.2_mean_value_theorem.pdf|Classroom Slides PDF]] \\ ===== The Shape of a Graph ===== {{youtube>npez7AKzCfM}} {{youtube>IsQ6Zi-g51Q}} \\ //Section 3.3 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ * If the derivative is positive on an interval, the original function is increasing on that interval. If the derivative is negative on an interval, the original function is decreasing on that interval.\\ * Concavity describes the direction a function is bending. A function is concave up on an interval, if the second derivative is positive on that interval and the function bends upwards. A function is concave down on an interval, if the second derivative is negative on that interval and the function bends downwards. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.3_graph_shape.pdf|Classroom Slides PDF]] \\ ===== Horizontal Asymptotes ===== {{youtube>E29ZLZ_EoCI}} {{youtube>BoJbExhO5rI}} \\ //Section 3.4 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ * The end behavior of a function is described with limits.\\ * Horizontal asymptotes of power functions are either zero or do not exist (tend towards infinity).\\ * Determinate and indeterminate forms.\\ [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.4_horizontal_asymptotes.pdf|Classroom Slides PDF]] \\ ===== Curve Sketching ===== {{youtube>hfkgjFf2vLU}} //Section 3.5 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ * The basics of curve sketching. \\ ===== Optimization ===== {{youtube>U1t1dJbQtgg}} //Section 3.7 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ * Optimized solutions to problems are found at critical points. This technique is useful in obtaining information in natural, less mathematical, settings.\\ [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.7_optimization.pdf|Classroom Slides PDF]] \\ ===== Antiderivatives ===== {{youtube>tzjvqUO2kDM}} //Section 3.9 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ * Antiderivatives of a function f(x) are functions whose derivative is f(x).\\ * The antiderivatives of a function differ by only a constant.\\ * Antiderivatives of common functions.\\ [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.9_antiderivatives.pdf|Classroom Slides PDF]] \\