Open intervals of increasing, decreasing & constant functions

Slides:



Advertisements
Similar presentations
Business Calculus Extrema. Extrema: Basic Facts Two facts about the graph of a function will help us in seeing where extrema may occur. 1.The intervals.
Advertisements

Find the solutions. Find the Vertex and Max (-1, 0) (5, 0) (2, 10)
Each part of graph is described as: 1)Increasing : function values increase from left to right 2)Decreasing: function values decrease 3)Constant function.
7.2 Polynomial Functions and Their Graphs
Basic Spreadsheet Functions Objective Functions are predefined formulas that perform calculations by using specific values, called arguments, in.
To solve equations using Intersect method with a graphing calculator Process 1.Enter y 1 = (left side of the equation). ENTER 2.Enter y 2 = (right side.
6 Parent Graphs. Class Work Work Book p. 39 #1 – 8, 13 – 24.
More on Functions and Their Graphs Section 1.3. Objectives Calculate and simplify the difference quotient for a given function. Calculate a function value.
OBJECTIVES: 1. DETERMINE WHETHER A GRAPH REPRESENTS A FUNCTION. 2. ANALYZE GRAPHS TO DETERMINE DOMAIN AND RANGE, LOCAL MAXIMA AND MINIMA, INFLECTION POINTS,
Chapter 4 Section 4-1 Solving Quadratic Equations in Calculator.
P.O.D. Using your calculator find the domain and range of: a) b) c)
September 17, 2012 Analyzing Graphs of Functions
Jeopardy Review Algebra 2.
AP CALCULUS AB Chapter 4: Applications of Derivatives Section 4.1:
Section 5.1 – Increasing and Decreasing Functions The First Derivative Test (Max/Min) and its documentation 5.2.
September 18, 2012 Analyzing Graphs of Functions Warm-up: Talk to your group about the Distance Formula worksheet given last week. Make sure you understand.
Today in Pre-Calculus Go over homework Notes: Finding Extrema –You’ll need a graphing calculator (id’s please) Homework.
PreCalculus Sec. 1.3 Graphs of Functions. The Vertical Line Test for Functions If any vertical line intersects a graph in more than one point, the graph.
Increasing/ Decreasing
Standard Form. Quadratic Function Highest degree is 2. Its graph is called a parabola. quadratic term linear term constant term.
Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.
Warm up The domain of a function is its a)y-values b) x-values c) intercepts  The range of a function is its a) y-values b) x-values c) intercepts.
POLYNOMIALS REVIEW The DEGREE of a polynomial is the largest degree of any single term in the polynomial (Polynomials are often written in descending order.
Graphing Calculator Steps Steps to follow to find the vertex of a parabola & to find the zeros of a parabola. Make sure you view this in presentation mode.
POLYNOMIALS REVIEW The DEGREE of a polynomial is the largest degree of any single term in the polynomial (Polynomials are often written in descending order.
Domain and Range: Graph Domain- Look horizontally: What x-values are contained in the graph? That’s your domain! Range- Look vertically: What y-values.
Polynomials. Polynomial  “many terms” The Degree of a polynomial is the largest degree of any single term – Examples:  has a degree of 5 The Leading.
Chapter 4: Polynomials Quadratic Functions (Section 4.1)
Sketching Functions We are now going to use the concepts in the previous sections to sketch a function, find all max and min ( relative and absolute ),
7/6/ & & 9-2 Polynomial Models & Their Graphs.
Do Now from 1.2a Find the domain of the function algebraically and support your answer graphically. Find the range of the function.
Increasing/decreasing and the First Derivative test
POLYNOMIALS REVIEW The DEGREE of a polynomial is the largest degree of any single term in the polynomial (Polynomials are often written in descending order.
Maxima and Minima of Functions
4.1 Graphing Quadratic Functions
EXTREMA and average rates of change
Today in Pre-Calculus Go over homework Need a calculator
Graph Vocabulary and Interpreting Graphs of Functions
3-6 Critical Points and Extrema
Absolute or Global Maximum Absolute or Global Minimum
Let’s Review Functions
3.1 Extreme Values Absolute or Global Maximum
3.6 Critical Points.
TOPICS ON CHAPTER 4 TEST: 1
Extreme Values of Functions
A function f is increasing on an open interval I if, for any choice of x1 and x2 in I, with x1 < x2, we have f(x1) < f(x2). A function f is decreasing.
Interpreting Graphs of Functions
Warm-up: Determine whether the graph of y is a function of x:
Characteristics of Polynomials: Domain, Range, & Intercepts
Analyzing the Graphs of Functions
Characteristics of Polynomials: Domain, Range, & Intercepts
5.2 Section 5.1 – Increasing and Decreasing Functions
7.2 Graphing Polynomial Functions
Section 2.3 – Analyzing Graphs of Functions
Section 4.4 – Analyzing Graphs of Functions
58 – First Derivative Graphs Calculator Required
Intervals of Increase and Decrease
4.3 Connecting f’ and f’’ with the graph of f
Unit 1 Day 1 Key Features of Graphs
Critical Numbers – Relative Maximum and Minimum Points
Functions and Their Graphs
Derivatives and Graphing
(3, 2) 2 -3 (-4, -3) -2 (5, -2) 1. a) Find: f(3) = ______
Characteristics of Polynomials: Domain, Range, & Intercepts
Determine whether the statement is sometimes, always, or never true
Warm up  .
Analyzing f(x) and f’(x) /
Let’s Review Functions
Let’s Review Functions
Let’s Review Functions
Presentation transcript:

Open intervals of increasing, decreasing & constant functions X values (left most point, right most point) Looking from left to right Increasing: Constant: Decreasing:

Relative Maximum & Minimums Relative Maximums: High point of a curve Relative Minimum: Low point of a curve Absolute Maximum: Highest point of the entire function, if it exists. Absolute Minimum: Lowest point of the entire function, if it exists.

Finding relative maximums and minimums with the calculator 1.) Enter function into editor Get y alone : y= 2.) 2nd trace 3:minimum or 4:maximum 3.) move cursor just to left side of max or min 4.) “enter” 5.) move cursor just to right side 6.) “enter” 7.) guess – “enter”

Example Rel. max= Rel. min= Absolute max= Absolute min= Open intervals of Increasing: Decreasing: Constant: