C957-Concavity-Slides PDF

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Concavity

Concavity C957 Applied Algebra Module 8: Interpreting Concavity for Polynomial Functions Module 15: Interpreting Concavity for Logistic Functions Module 19: Interpreting Concavity for Situations

Increasing Functions

Decreasing Functions

Concave Up/Down

Exercise 1

This graph shows a polynomial function that models a company's revenue in the years since 2000. Using the points A through G, give a pair of points between which th function is: 1) Concave Up 2) Decreasing Faster and Faster 3) Increasing Slower and Slower 4) Increasing Concave Up 5) Decreasing Slower and Slower

Function Types

Inflection Points

The logistic function graphed here shows the relationship between a company's profit an the amount of money they spend on advertising. Find the inflection point and interpret its meaning.

Exercise 2

For the graph pictured here, use th terminology that we've discussed t describe the following: 1.) The interval [2, 5]

2.) The interval [6, 9]

3.) The interval [13, 15.5]

4.) The point (18.5, 10)

Exercise 3

Suppose we have functions modelling each of the following scenarios In an ideal situation, would the function be increasing or decreasing? Would it be Concave Up or Concave Down? 1.) The altitude of a plane coming in for a landing Increasing/Decreasing

Concave Up/Down

2.) The profit for your business Increasing/Decreasing

Concave Up/Down

3.) The termite population in your house Increasing/Decreasing

Concave Up/Down...