Derivative and Nature of the Curve of a Function

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Mathematical Methods for Economics I

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What is a Straight Line? A straight line is a locus of all points such that the moving point does not change its direction, or the rate of change of direction remains constant. In other words, a straight line is a line of zero curvature. Precisely, a straight line is the shortest distance between two points in a plane. The general form of a straight line in two-dimensional Cartesian coordinates is: 𝑦 = 𝑚𝑥 + 𝑐 Where: 𝑚 = the slope or gradient of the line. 𝑐 = the y-intercept, i.e., the value of 𝑦 where the graph of the line crosses the y-axis. What is Curvature? Curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. A straight line has zero curvature, which means it does not bend. Plotting a Straight Line Let us take a simple linear equation: 𝑦 = 2𝑥 + 1 Computing the values of y y  for various x x : When x = 0 x = 0 : y = 2 ( 0 ) + 1 = 1 When x = 1: y = 2 ( 1 ) + 1 = 3 When x = 2 x = 2 : y = 2 ...
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