0 Are You Ready For This Course? PL Prologue: Principles Of Problem Solving P Prerequisites 1 Equations And Graphs 2 Functions 3 Polynomial And Rational Functions 4 Exponential And Logarithmic Functions 5 Trigonometric Functions: Right Triangle Approach 6 Trigonometric Functions: Unit Circle Approach 7 Analytic Trigonometry 8 Polar Coordinates And Parametric Equations 9 Vectors In Two And Three Dimensions 10 Systems Of Equations And Inequalities 11 Matrices And Determinants 12 Conic Sections 13 Sequences And Series 14 Counting And Probability A Geometry Review B Calculations And Significant Figures C Graphing With A Graphing Calculator Chapter2: Functions
2.1 Functions 2.2 Graphs Of Functions 2.3 Getting Information From The Graph Of A Function 2.4 Average Rate Of Change Of A Function 2.5 Linear Functions And Models 2.6 Transformations Of Functions 2.7 Combining Functions 2.8 One-to-one Functions And Their Inverses 2.CR Chapter Review 2.CT Chapter Test 2.FOM Focus On Modeling: Modeling With Functions Section2.4: Average Rate Of Change Of A Function
Problem 1E Problem 2E Problem 3E Problem 4.1E: aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line... Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________. Problem 5.1E: 5-6 Yes or No? If No, give a reason aIs the average rate of change of a function between x=a and x=b... Problem 5.2E Problem 6.1E Problem 6.2E Problem 7E Problem 8E: 7-10 Net Change and Average Rate of Change The graph of a function is given. Determine a the net... Problem 9E: 7-10 Net Change and Average Rate of Change The graph of a function is given. Determine a the net... Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E Problem 28E: Average Rate of Change Graphs of the functions f, g, and h are shown below. What can you say about... Problem 29E: Changing Water Levels The graph shows the depth of water W in a reservoir over a one-year period as... Problem 30E: Population Growth and Decline The graph shows the population P in a small industrial city from 1950... Problem 31E Problem 32E: Running Speed A man is running around a circular track that is 200 m in circumference. An observer... Problem 33E: DVD Player Sales The table shows the number of DVD players sold in a small electronics store in the... Problem 34E Problem 35E: Cooling Soup When a bowl of hot soup is left in a room, the soup eventually cools down to room... Problem 36E: Farms in the United States The graph gives the number of farms in the United States from 1850 to... Problem 37E: Three-Way Tie A downhill skiing race ends in a three-way tie for first place. The graph shows... Problem 38E: Speed Skating Two speed skaters, A and B, are racing in a 500-m event. The graph shows the distance... Problem 39E Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Find the equation of normal to the function f(x)=x3−3x+1�(�)=�3−3�+1 at its local maximum point.
Transcribed Image Text: Find the equation of normal to the function f(x) = x³ - 3x + 1 at its local
maximum point.
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
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