We reviwed the basic rules of concavity, if the curve is concave up then; the tangent lines lie beneath the curve, f` is increasing, and f`` is postive. If the curve is concave up then; the tangent lines lie above the curve, f` is decreasing and f`` is negative. Also an inflection point is known as the point on a curve when the concavity changes. At the inflection point the tangent lines lie both above and below the curve. We also dicussed how before 1992, scientific graphing calculators were not used by most students, therefore they used to have another method for creating an acurate sketch of the graph of f(x). They would use f` and f`` to sketch the graphs. You had to locate the maximum point, the minimum point, and the inflection point. You could estimate where the graph of f(x) would be incresing and decreasing by finding f` then creating a number line and pluging in values (horizontal line test from FST). While this is good information it is not enough to create a graph therefore we need to use f`` which we will talk about tommorow.
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We reviwed the basic rules of concavity, if the curve is concave up then; the tangent lines lie beneath the curve, f` is increasing, and f`` is postive. If the curve is concave up then; the tangent lines lie above the curve, f` is decreasing and f`` is negative. Also an inflection point is known as the point on a curve when the concavity changes. At the inflection point the tangent lines lie both above and below the curve.
We also dicussed how before 1992, scientific graphing calculators were not used by most students, therefore they used to have another method for creating an acurate sketch of the graph of
f(x). They would use f` and f`` to sketch the graphs. You had to locate the maximum point, the minimum point, and the inflection point. You could estimate where the graph of f(x) would be incresing and decreasing by finding f` then creating a number line and pluging in values (horizontal line test from FST). While this is good information it is not enough to create a graph therefore we need to use f`` which we will talk about tommorow.
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