'Concavity' presentation slideshows

CHAPTER 3 SECTION 3.4 CONCAVITY AND THE SECOND DERIVATIVE TEST

CHAPTER 3 SECTION 3.4 CONCAVITY AND THE SECOND DERIVATIVE TEST. Definition of Concavity and Figure 3.24. Sketch 4 graphs a)1 decreasing and concave up b)1 increasing and concave up, c)1 decreasing and concave down, d)1 increasing and concave down. y. y. x. x. b. a. y. y. x. x. d. c.

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Concavity and Inflection Points

Concavity and Inflection Points. The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Concavity and Inflection Points.

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Who wants to be a Millionaire?

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How to find the absolute minimum and maximum values

4.1. How to find the absolute minimum and maximum values. The closed interval method:. Continues function on a closed interval [ a,b ] . 1)Find the values of f at the critical numbers of f in ( a,b ). 2)Find the end values of the end points of the interval .

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3.2 Graphs of Functions

3.2 Graphs of Functions. Objectives: Determine whether a graph represents a function. Analyze graphs to determine domain and range, local maxima and minima, inflection points, and intervals where they are increasing, decreasing, concave up, and concave down. Graph parametric equations.

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Applications of Derivatives

Applications of Derivatives. Curve Sketching. What the First Derivative Tells Us:. Suppose that a function f has a derivative at every point x of an interval I. Then:. What This Means:.

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Sec 3.4: Concavity and the Second Derivative Test

Sec 3.4: Concavity and the Second Derivative Test. Determine intervals on which a function is concave upward or concave downward. Find any points of inflection of the graph of a function. Apply the Second Derivative Test to find relative extrema of a function. Definition of Concavity.

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Miss Battaglia AP Calculus AB/BC

3.4 Concavity and the Secondary Derivative Test Objective: Determine on intervals on which a function is concave up or down; find any points of inflection; apply the Second Derivative Test. Miss Battaglia AP Calculus AB/BC. Definition of Concavity.

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C.5 Concavity and the Second Derivative Test

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3.4 Concavity and the Second Derivative Test

3.4 Concavity and the Second Derivative Test. Determining Concavity. Determine the open intervals on which the graph is concave up or concave down. Determining Concavity. Determine the intervals on which the graph is concave up or concave down. Finding Points of Inflection.

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Concavity and the Second Derivative Test

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Second Derivative Test

Second Derivative Test. Concavity. If the graph of a function f lies above all of its tangents, then it is called concave upward If the graph of a function f lies below all of its tangents, then it is called concave downward. Test for Concavity.

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Concavity and Rates of Change

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