'Graph changes' presentation slideshows

Graphs

Graphs. 2012. Question One. (a) The table below gives the adult single train fares for travel from the centre of a city. . ( i ) On the grid below, sketch the graph of the adult train fares against the number of stations from the centre of the city. .

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STA 291 Lecture 5 Chap 4

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Lecture 1(c) Marginal Analysis and Optimization

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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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Section 3-6

Section 3-6. Critical Points and Extrema. Vocabulary. Critical Points Maximum Minimum Absolute Maximum Absolute Minimum Point of Inflection Relative Extrema Relative Maximum Relative Minimum. Maximum. Minimum. Point of Inflection. Review. Maximum: increasing to the left

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2.2

2.2. The Derivative as a Function. The Derivative as a Function. We have considered the derivative of a function f at a fixed number a : Here we change our point of view and let the number a vary. If we replace a in Equation 1 by a variable x , we obtain.

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Writing Piecewise Functions

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Polynomial Functions and Models

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Random-Graph Theory

Random-Graph Theory. The Erdos-Renyi model.

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3.6 Critical Points

3.6 Critical Points. Critical Points. . Maximum : When the graph is increasing to the left of x = c and decreasing to the right of x = c (top of hill) Minimum : When the graph of a function is decreasing to the left of x = c and increasing ot the right of x = c (bottom of valley)

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Quadratic Functions

Quadratic Functions. Unit Objectives: Solve a quadratic equation. Graph/Transform quadratic functions with/without a calculator Identify function attributes: domain, range, vertex, line of symmetry, number and nature of roots, maximum/minimum values.

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Section 4.4 Concavity and Second Derivative Test

Section 4.4 Concavity and Second Derivative Test. Definition. A function f ( x ) is concave up on an interval ( a,b ) if the graph of f ( x ) lies above its tangent line at each point on ( a,b ).

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