MAT 1339 Lecture 12: MAT1339 - Lecture 10 - Critical points and the second derivative (1)
3 Dec 2018
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Mat1339 - lecture 10 - critical points and the second derivative. Non-extremal critical points: a point is not an extrema if the tangent line is horizontal but it does not change sign or if the tangent line is vertical and the slope is undefined. Side-note: the extrema must be in the domain f(x). So if f(x) is undefined at x = c, then c is automatically neither even if there"s no jump or asymptotes. Example: f(x) is defined and f"(x) is undefined. Taxonomy of critical points assuming f(x) is defined: What f"" tells us: how to connect dots. f"" take the derivative of the derivative. Side-note: in all 3 possible shapes the tangent lines have a positive slope at every x. A function is neither if because f" is a constant. To see the shape of the graph, compute the increasing/decreasing intervals on the same chart.
