BIOL 1111 Lecture Notes - Lecture 1: Mean Value Theorem, Maxima And Minima

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Laws/theorems/de nitions for curve sketching: de nition: (a) if the graph of f lies above all of its tangents on an interval i, then it is called concave upward on i. If f (x) < 0 on an interval, then f is decreasing on that interval. (f) concavity test: if f (x) > 0 on an interval, then f is concave upward on that interval. If f (x) < 0 on an interval, then f is concave downward on that interval. (g) minima/maxima test: first derivative test: suppose c is a critical number of a continuous function f .

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