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CalculusCalculus (MindTap Course List)Slope of a Tangent Line Sketch the graph of the function f ( x ) = x and label the point (4, 2) on the graph. (a) Find the slope of the line joining (4, 2) and (9, 3). Is the slope of the tangent line at (4, 2) greater than or less than this number? (b) Find the slope of the line joining (4, 2) and (1, 1). Is the slope of the tangent line at (4, 2) greater than or less than this number? (c) Find the slope of the line joining (4, 2) and (4.41, 2.1). Is the slope of the tangent line at (4, 2) greater than or less than this number? (d) Find the slope of the line joining (4, 2) and (4 + h, f (4+ h )) in terms of the nonzero number h. (e) What is the slope of the tangent line at (4, 2)? Explain how you arrived at your answer.BuyFind*arrow_forward*

11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275347

Chapter P, Problem 10PS

Textbook Problem

**Slope of a Tangent Line** Sketch the graph of the function

(a) Find the slope of the line joining (4, 2) and (9, 3). Is the slope of the tangent line at (4, 2) greater than or less than this number?

(b) Find the slope of the line joining (4, 2) and (1, 1). Is the slope of the tangent line at (4, 2) greater than or less than this number?

(c) Find the slope of the line joining (4, 2) and (4.41, 2.1). Is the slope of the tangent line at (4, 2) greater than or less than this number?

(d) Find the slope of the line joining (4, 2) and (4 + *h, f*(4+*h*)) in terms of the nonzero number *h.*

(e) What is the slope of the tangent line at (4, 2)? Explain how you arrived at your answer.

Calculus (MindTap Course List)

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Ch. P.1 - Finding Intercepts Describe how to find the x- and...Ch. P.1 - CONCEPT CHECK Verifying Points of Intersection How...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Matching In Exercises 3-6, match the equation with...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...Ch. P.1 - Sketching a Graph by Point Plotting In Exercises...

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P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Finding Parallel and Perpendicular Lines In...Ch. P.2 - Rate of Change In Exercises 63 and 64, you are...Ch. P.2 - Rate of Change In Exercises 63 and 64, you are...Ch. P.2 - Collinear Points In Exercises 65 and 66. determine...Ch. P.2 - Collinear Points In Exercises 65 and 66. determine...Ch. P.2 - Square Show that the points (-1, 0),(3, 0),(1, 2),...Ch. P.2 - Analyzing a Line A line is represented by the...Ch. P.2 - Tangent Line Find an equation of the line tangent...Ch. P.2 - Tangent Line Find an equation of the line tangent...Ch. P.2 - Finding Points of Intersection Find the...Ch. P.2 - HOW DO YOU SEE IT? Several lines are shown in the...Ch. P.2 - Temperature Conversion Find a linear equation that...Ch. P.2 - Choosing a Job As a salesperson, you receive a...Ch. P.2 - Apartment Rental A real estate office manages an...Ch. P.2 - Modeling Data An instructor gives regular 20-point...Ch. 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P.3 - Using the Vertical Line Test In Exercises 39-42,...Ch. P.3 - Using the Vertical Line Test In Exercises 39-42....Ch. P.3 - Using the Vertical Line Test In Exercises 39-42....Ch. P.3 - Deciding Whether an Equation Is a Function In...Ch. P.3 - Deciding Whether an Equation Is a Function In...Ch. P.3 - Deciding Whether an Equation Is a Function In...Ch. P.3 - Deciding Whether an Equation Is a Function In...Ch. P.3 - Transformation of a Function In Exercises 47-50,...Ch. P.3 - Transformation of a Function In Exercises 47-50,...Ch. P.3 - Transformation of a Function In Exercises 47-50,...Ch. P.3 - Transformation of a Function In Exercises 47-50,...Ch. P.3 - Matching In Exercises 51-56, use the graph of...Ch. P.3 - Matching In Exercises 51-56, use the graph of...Ch. P.3 - Matching In Exercises 51-56, use the graph of...Ch. P.3 - Matching In Exercises 51-56, use the graph of...Ch. P.3 - Matching In Exercises 51-56, use the graph of...Ch. P.3 - Matching In Exercises 51-56, use the graph of...Ch. P.3 - Sketching Transformations Use the graph of f shown...Ch. P.3 - Sketching Transformations Use the graph of f shown...Ch. P.3 - Combinations of Functions In Exercises 59 and 60,...Ch. P.3 - Combinations of Functions In Exercises 59 and 60,...Ch. P.3 - Evaluating Composite Functions Given f(x)=x and...Ch. P.3 - Evaluating Composite Functions Given f(x)=2x3 and...Ch. P.3 - Finding Composite Functions In Exercises 63-66,...Ch. P.3 - Finding Composite Functions In Exercises 63-66,...Ch. P.3 - Finding Composite Functions In Exercises 63-66,...Ch. P.3 - Finding Composite Functions In Exercises 63-66,...Ch. P.3 - Evaluating Composite Functions Use the graphs of f...Ch. P.3 - Ripples A pebble is dropped into a calm pond,...Ch. P.3 - Think About It In Exercises 69 and 70, F(x)=fgh....Ch. P.3 - Think About It In Exercises 69 and 70, F(x)=fgh)....Ch. P.3 - Think About It In Exercises 71 and 72, find the...Ch. 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P.4 - Degrees to Radians In Exercises 11 and 12, convert...Ch. P.4 - Degrees to Radians In Exercises 11 and 12, convert...Ch. P.4 - Completing a Table Let r represent the radium of a...Ch. P.4 - Angular Speed A car is moving at the rate of 50...Ch. P.4 - Evaluating Trigonometric Functions In Exercise 15...Ch. P.4 - Evaluating Trigonometric Functions In Exercise 15...Ch. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Evaluating Trigonometric Functions In Exercises...Ch. P.4 - Evaluating Trigonometric Functions Using...Ch. P.4 - Evaluating Trigonometric Functions Using...Ch. 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P.4 - Sketching the Graph of a Trigonometric Function In...Ch. P.4 - Sketching the Graph of a Trigonometric Function In...Ch. P.4 - Sketching the Graph of a Trigonometric Function In...Ch. P.4 - Sketching the Graph of a Trigonometric Function In...Ch. P.4 - Sketching the Graph of a Trigonometric Function In...Ch. P.4 - Sketching the Graph of a Trigonometric Function In...Ch. P.4 - Sketching the Graph of a Trigonometric Function In...Ch. P.4 - Graphical Reasoning In Exercises 67 and 68, find...Ch. P.4 - Graphical Reasoning In Exercises 67 and 68, find...Ch. P.4 - Think About It You are given die value of tan. Is...Ch. P.4 - EXPLORING CONCEPTS Restricted Domain Explain how...Ch. P.4 - EXPLORING CONCEPTS Think About It How do the...Ch. P.4 - HOW DO YOU SEE IT? Consider an angle in standard...Ch. P.4 - Think About It Sketch the graphs of...Ch. P.4 - Ferris Wheel The model for the height h of a...Ch. P.4 - Sales The monthly sales S (in thousands of units)...Ch. P.4 - Pattern Recognition Use a graphing utility to...Ch. P.4 - True or False? In Exercises 7780, determine...Ch. P.4 - True or False? In Exercises 77-80, determine...Ch. P.4 - True or False? In Exercises 77-80, determine...Ch. P.4 - True or False? In Exercises 77-80, determine...Ch. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Finding Intercepts In Exercises 1-4, find any...Ch. P - Testing for Symmetry In Exercises 5-8, test for...Ch. P - Testing for Symmetry In Exercises 5-8, test for...Ch. P - Testing for Symmetry In Exercises 5-8, test for...Ch. P - Testing for Symmetry In Exercises 5-8, test for...Ch. P - Using Intercepts and Symmetry to Sketch a Graph in...Ch. P - Using Intercepts and Symmetry to Sketch a Graph in...Ch. P - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P - Using Intercepts and Symmetry to Sketch a Graph in...Ch. P - Using Intercepts and Symmetry to Sketch a Graph In...Ch. P - Using Intercepts and Symmetry to Sketch a Graph in...Ch. P - Finding Points of Intersection In Exercises 15-18,...Ch. P - Finding Points of Intersection In Exercises 15-18,...Ch. P - Finding Points of Intersection In Exercises 15-18,...Ch. P - Finding Points of Intersection In Exercises 15-18,...Ch. P - Finding the Slope of a Line In Exercises 19 and...Ch. P - Finding the Slope of a Line In Exercises 19 and...Ch. P - Finding an Equation of a Line In Exercises 21-24,...Ch. P - Finding an Equation of a Line In Exercises 21-24,...Ch. P - Finding an Equation of a Line In Exercises 21-24,...Ch. P - Finding an Equation of a Line In Exercises 21-24,...Ch. P - Finding the Slope and y-Intercept In Exercises 25...Ch. P - Finding the Slope and y-Intercept In Exercises 25...Ch. P - Sketching a Line in the Plane In Exercises 27-30,...Ch. P - Sketching a Line in the Plane In Exercises 27-30,...Ch. P - Sketching a Line in the Plane In Exercises 27-30,...Ch. P - Sketching a Line in the Plane In Exercises 27-30,...Ch. P - Finding an Equation of a Line In Exercises 31 and...Ch. P - Finding an Equation of a Line In Exercises 31 and...Ch. P - Finding Equations of Lines Find equations of the...Ch. P - Finding Equations of Lines Find equations of the...Ch. P - Rate of Change The purchase price of a new machine...Ch. P - Break-Even Analysis A contractor purchases a piece...Ch. P - Evaluating a Function In Exercises 37-40, evaluate...Ch. P - Evaluating a Function In Exercises 37-40, evaluate...Ch. P - Evaluating a Function In Exercises 37-40, evaluate...Ch. P - Evaluating a Function In Exercises 37-40, evaluate...Ch. P - Finding the Domain and Range of a Function In...Ch. P - Finding the Domain and Range of a Function In...Ch. P - Finding the Domain and Range of a Function In...Ch. P - Finding the Domain and Range of a Function In...Ch. 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