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[DOC File]New Chapter 3
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We can construct a second derivative chart as shown in figure 6.___ below to help us organize this information. (Figure 6.__ Second derivative chart for graph given in example 6.___ Behavior of test point n/a n/a n/a Sign of + – + The second derivative chart reveals that has two points of inflection, one at x = 2 and the other at x = 6.
second derivative graph

[DOC File]Math 202 – Test 2 Review
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If the second derivative is negative, the graph is concave down at that point and the point is a maximum. If the second derivative is positive, the graph is concave up at that point and the point is a minimum. Recognize that an inflection point occurs where a function changes from concave up to concave down (or vice versa).
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[DOC File]Derivatives - UH
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The derivative is a calculated quantity that tells you the slope of the tangent line to any point on the graph. The definition of a derivative is taking a limit as h approaches zero, but we’ll use the shortcuts to find them. This is the instantaneous rate of change of the graph at a chosen point.
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[DOC File]Section 1 - Radford
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Inflection points are points where the concavity of the graph of a function f changes. Note: If is a point of inflection of the graph of f , then either or is undefined. Second Derivative Test (Test For Relative Maximum and Relative Minimum Points) Let f be a function where x = c is a critical point where . 1. If , then is a relative minimum. 2.
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[DOC File]Calculus 2 Lecture Notes, Section 9.2
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The second derivative tells us what it always told us: the concavity of the graph and the location of critical points where the graph may change concavity. Practice: Find an expression for the second derivative of a unit circle at the origin described by parametric equations, and then analyze the expression in terms of concavity.
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Activity overview:
On page 2.2, choose ‘show=2’ to display the graph of the second derivative for the same function. How did you verify your solution using the graph of the second derivative? Problem 3 – Finding points of inflection algebraically Advance to page 3.1. A function and its first and second derivatives are shown.
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Finding second derivative from graph