Explanation The total change in the dependent variable over the total change in the independent variable is called the average rate of change. The average rate of change between two points of a function is given by: f ( x 2 ) − f ( x 1 ) x 2 − x 1 , Where, ( x 1 , f ( x 1 ) ) is the starting point of the interval and ( x 2 , f ( x 2 ) ) is the endpoint of the interval. The average rate of change of a function can be negative, positive, or even zero just like the slope of the secant line. To know how fast the particle moves at a particular instant of time, we define Instantaneous rate of change. Given: Q ( t ) = t 2 . Formula used: The average rate of change of Q ( t ) with respect to t is given by: Δ Q ( t ) Δ t = Q ( t 2 ) − Q ( t 1 ) t 2 − t 1 Calculation: The average rate of change of Q over the interval [ 1 , t ] is: Δ Q ( t ) Δ t = Q ( t ) − Q ( 1 ) t − 1 = t 2 − ( 1 ) 2 t − 1 = ( t + 1

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 2.1, Problem 29E

To determine

A formula for the slope of secant line over the interval [1,t] and use it to estimate the slope of tangent at t=1.

Also, repeat formula for the given interval [2,t] and for the slope of the tangent t=2.

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Chapter 2.1, Problem 28E

Chapter 2.1, Problem 30E

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Chapter 2 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E

Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.2 - Prob. 1PQ Ch. 2.2 - Prob. 2PQ Ch. 2.2 - Prob. 3PQ Ch. 2.2 - Prob. 4PQ Ch. 2.2 - Prob. 5PQ Ch. 2.2 - Prob. 6PQ Ch. 2.2 - Prob. 7PQ Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - 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A formula for the slope of secant line over the interval [ 1 , t ] and use it to estimate the slope of tangent at t = 1 . Also, repeat formula for the given interval [ 2 , t ] and for the slope of the tangent t = 2 .

Solution Summary: The author explains the formula for the slope of secant line over the interval left[1,tright] and the tangent's slope. The average rate of change of a function can be negative,

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A formula for the slope of secant line over the interval [1,t] and use it to estimate the slope of tangent at t=1.

Also, repeat formula for the given interval [2,t] and for the slope of the tangent t=2.

Want to see the full answer?

Chapter 2 Solutions

A formula for the slope of secant line over the interval [ 1 , t ] and use it to estimate the slope of tangent at t = 1 . Also, repeat formula for the given interval [ 2 , t ] and for the slope of the tangent t = 2 .

Solution Summary: The author explains the formula for the slope of secant line over the interval left[1,tright] and the tangent's slope. The average rate of change of a function can be negative,

Concept explainers

Videos

A formula for the slope of secant line over the interval [1,t] and use it to estimate the slope of tangent at t=1. Also, repeat formula for the given interval [2,t] and for the slope of the tangent t=2.

Want to see the full answer?

Chapter 2 Solutions

A formula for the slope of secant line over the interval [1,t] and use it to estimate the slope of tangent at t=1.

Also, repeat formula for the given interval [2,t] and for the slope of the tangent t=2.