Explanation 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 the instantaneous rate of change. Given: f ( t ) = 12 t − 7 ; t = − 4 Formula Used: The average rate of change of f ( t ) with respect to t is given by: Δ f Δ t = f ( t 2 ) − f ( t 1 ) t 2 − t 1 Calculation: To compute the instantaneous rate of change of f ( t ) = 12 t − 7 at the point t = − 4 , first compute the average rate of change between two points

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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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 2.1, Problem 13E

To determine

The instantaneous rate of change at the point indicated.

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Chapter 2.1, Problem 12E

Chapter 2.1, Problem 14E

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Chapter 2 Solutions

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The instantaneous rate of change at the point indicated.

Solution Summary: The author explains that the instantaneous rate of change of f(t)=12t-7 is 12; the average rate between two points can be negative, positive, or even zero.

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The instantaneous rate of change at the point indicated.

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Chapter 2 Solutions