Instantaneous Rate Of Change
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The graph shows y = f(x) in purple. Which line has a slope equal to the rate expression shown?
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Line a
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Line b
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Line c
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Line d
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Can you interpret and/or estimate instantaneous rate of change in multiple representations?
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- 2.
Estimate the instantaneous rate using the graph of y = f(x).
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0.02
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–0.02
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7.25
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–7.25
Correct Answer
A. –7.25Explanation
The correct answer is -7.25. This is because the graph of y = f(x) has a steep negative slope at the given point, indicating a high rate of change in the negative direction. Therefore, the instantaneous rate at this point is -7.25.Rate this question:
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- 3.
Estimate the instantaneous rate of change of H(x) = sin(ln x2) at x = –3
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0.1
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0.4
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0.8
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3.5
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Undefined
Correct Answer
A. 0.4Explanation
The instantaneous rate of change of a function at a specific point can be found by taking the derivative of the function and evaluating it at that point. In this case, the function H(x) = sin(ln x^2) needs to be differentiated. The derivative of sin(x) is cos(x), and the derivative of ln(x^2) is 2/x. Therefore, the derivative of H(x) is cos(ln x^2) * 2/x. Evaluating this derivative at x = -3 gives cos(ln 9) * 2/-3. Since cos(ln 9) is a constant value, the instantaneous rate of change at x = -3 is 2/(-3) = -2/3. None of the given answer choices match this value, so the correct answer is undefined.Rate this question:
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- 4.
Acceleration is the rate of change of velocity. If the velocity of a car driving on a straight road is given by v(t), which of the following expressions represent the car's instantaneous expression at t = 5 seconds? (Check all that apply.)
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Expression 1:
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Expression 2:
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Expression 3:
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Expression 4:
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Expression 5:
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Expression 6:
Correct Answer(s)
A. Expression 3:
A. Expression 4:
A. Expression 6:Explanation
The expressions that represent the car's instantaneous acceleration at t = 5 seconds are Expression 3, Expression 4, and Expression 6.Rate this question:
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- 5.
Which statement(s) correctly contrast average rate of change and instantaneous rate of change?
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Average rate of change requires specifying two points on a graph while instantaneous rate of change requires only one.
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Average rate of change can be interpreted as a slope while instantaneous rate of change can not.
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Average rate of change can be for any function while instantaneous rate of change is only for nonlinear functions.
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Average rate of change can be calculated as a difference quotient while instantaneous rate of change is a limit of a difference quotient.
Correct Answer(s)
A. Average rate of change requires specifying two points on a graph while instantaneous rate of change requires only one.
A. Average rate of change can be calculated as a difference quotient while instantaneous rate of change is a limit of a difference quotient.Explanation
The correct answer states that average rate of change requires specifying two points on a graph while instantaneous rate of change requires only one. This is because average rate of change is calculated by finding the slope between two points on a graph, while instantaneous rate of change is the rate of change at a specific point on a graph. Additionally, the correct answer states that average rate of change can be calculated as a difference quotient, which is the change in the dependent variable divided by the change in the independent variable, while instantaneous rate of change is the limit of a difference quotient as the change in the independent variable approaches zero.Rate this question:
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Mar 21, 2023Quiz Edited by
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Aug 10, 2020Quiz Created by
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