(a) Explanation Given Information: The function is given as f ( x ) = x 3 The points are given as x 1 = 1.1 and x 0 = 1 The slope of the secant line is given by, m = Δ y Δ x = f ( x 1 ) − f ( x 0 ) x 1 − x 0 Now, f ( x 1 ) = ( 1 (b) To determine The slope of the line that is tangent to the graph when x = 1 and compare this slope with part (a).

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 3.1, Problem 40PS

(a)

To determine

The slope of the secant line joining the points on the graph of f whose x -coordinates are 1 and 1.1.

(b)

To determine

The slope of the line that is tangent to the graph when x = 1 and compare this slope with part (a).

Expert Solution & Answer

Chapter 3 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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The slope of the secant line joining the points on the graph of f whose x -coordinates are 1 and 1.1.

Solution Summary: The author explains the slope of the secant line joining the points on the graph of f whose x -coordinates are 1 and 1.1.

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The slope of the secant line joining the points on the graph of f whose x -coordinates are 1 and 1.1.

The slope of the line that is tangent to the graph when x = 1 and compare this slope with part (a).

Chapter 3 Solutions