Math 220 Calculus I Notes for Exam 1 It was the best of times it was the worst of times Things was real good things was turribel It was the best of times it was the worst of times Things was real good things was turribel Just as in any other class you have to use the vocabulary correctly and make the meaning of your answers clear Mathematics has its own grammar You need to know and use the vocabulary of calculus correctly f x y points on the curve graph f rate of change slope of the curve maximum minimum f concavity of the curve points of inflection You need to know and use the vocabulary of calculus correctly f is increasing f is decreasing f 0 f 0 f is positive f is negative You need to know and use the vocabulary of calculus correctly f 0 f 0 f has a minimum f is concave up f 0 f 0 f has a maximum f is concave down You need to know and use the vocabulary of calculus correctly f is concave up f is concave down f 0 f 0 f is positive f is a point of inflection f 0 f is zero f is negative You need to know and use the vocabulary of calculus correctly Both of these are points of inflection concavity changes f 0 f 0 f 0 f 0 At a point of inflection the first derivative could be anything f x F x A f x B Explain how you know f x because it is What is it A the function the graph the slope the first derivative the second derivative B f x at f at f A at point A at point B B at point A f x A horizontal tangent has no slope A A horizontal tangent has a slope 0 f 0 B at point A The curve changes from concave up to concave down Point A is a point of inflection f 0 f x A B at point B f x The curve has a horizontal tangent A Point B is a relative minimum point f 0 B at point B f x The curve is concave up f 0 A f is positive B In answering word problems applications it will be important to distinguish between amounts the function itself and a rate of change the derivative of the function
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