Instantaneous Rate Of Change

5 Questions | By I-heng_mccomb | Last updated: Mar 21, 2022 | Total Attempts: 614

Can you interpret and/or estimate instantaneous rate of change in multiple representations?

Questions and Answers

1.

The graph shows y = f(x) in purple. Which line has a slope equal to the rate expression shown?
- A.
  
  Line a
- B.
  
  Line b
- C.
  
  Line c
- D.
  
  Line d
2.

Estimate the instantaneous rate using the graph of y = f(x).
- A.
  
  0.02
- B.
  
  –0.02
- C.
  
  7.25
- D.
  
  –7.25
3.

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.)
- A.
  
  Expression 1:
- B.
  
  Expression 2:
- C.
  
  Expression 3:
- D.
  
  Expression 4:
- E.
  
  Expression 5:
- F.
  
  Expression 6:
4.

Estimate the instantaneous rate of change of H(x) = sin(ln x²) at x = –3
- A.
  
  0.1
- B.
  
  0.4
- C.
  
  0.8
- D.
  
  3.5
- E.
  
  Undefined
5.

Which statement(s) correctly contrast average rate of change and instantaneous rate of change?
- A.
  
  Average rate of change requires specifying two points on a graph while instantaneous rate of change requires only one.
- B.
  
  Average rate of change can be interpreted as a slope while instantaneous rate of change can not.
- C.
  
  Average rate of change can be for any function while instantaneous rate of change is only for nonlinear functions.
- D.
  
  Average rate of change can be calculated as a difference quotient while instantaneous rate of change is a limit of a difference quotient.

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