Exercises are given at the end. Increasing and Decreasing Functions, Min and Max, Concavity studying properties of the function using derivatives – Typeset by FoilTEX – 1. Read through each of the scenarios and choose the graph of the function that best matches the situation. For example, imagine you are at the store and you are buying some baseballs that costs $3 each. A monotonically decreasing function is always headed down; As x increases in the positive direction, f(x) always decreases.. Increasing and Decreasing Functions T/F: Functions always switch from increasing to decreasing, or decreasing to increasing, at critical points. A common misconception is to look at the squaring function and see two curves that symmetrically increase away from zero. 5. Let students work independently on Exercise 1; then, discuss and confirm answers as a class. Exercises 1. Present examples of functions that are constant; for example, your cell phone bill is $79 every month for unlimited calls and data. Consider f0(x) = 2x−5 Introduce the term constant function. Increasing and decreasing functions. Exercises 1. Increasing is where the function has a positive slope and decreasing is where the function has a negative slope. a. function tells them if the function is increasing or decreasing. We discuss the first derivative test and illustrate its use with several examples. All relative extrema of a functions’ graph must occur at critical numbers of the function (where the derivative is undefined or zero). • A linear function whose graph has a negative slope is said to be a decreasing function. Strictly Increasing Function. Examples Example 1. There are functions that are always increasing. Below is the graph of a quadratic function, showing where the function is increasing and decreasing. Give an example of a function describing a situation where it is “bad” to be increasing and “good” to be decreasing. A function is constant when the graph is a perfectly at horizontal line. Find where f(x) = x2 − 5x + 1 is increasing and where it is decreasing. The point where a graph changes direction from increasing to decreasing (or decreasing to increasing) is called a turning point or inflection point. For example: decreasing increasing constant decreasing increasing decreasing When we describe where the function is increasing, decreasing, and A function is decreasing when the graph goes down as you travel along it from left to right. Earlier, you were asked how to determine if a function is increasing or decreasing. A function can be decreasing at a specific point, for part of the function, or for the entire domain. Explain the reason behind each choice. Increasing and Decreasing Functions Lesson 5.1 The Ups and Downs Think of a function as a roller coaster going from left to right Uphill Slope > 0 Increasing function ... – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 3d5af0-NTFhN Lecture 9 - Increasing and Decreasing Functions, Extrema, and the First Derivative Test 9.1 Increasing and Decreasing Functions One of our goals is to be able to solve max/min problems, especially economics related examples. Increasing and Decreasing ... > 0(f0(x) < 0) ⇒ is increasing (decreasing) EXAMPLE 3. • A linear function whose graph has a zero slope is said to be a constant function. Increasing Function vs.