MHB Average Rate Of Change Formula

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SUMMARY

The average rate of change formula is defined as \(\frac{\Delta f}{\Delta x} = \frac{f(b)-f(a)}{b-a}\). This notation is widely accepted, with variations in symbols depending on the context. Greg's example represents the standard notation for average rate of change, emphasizing that while certain symbols are conventional, any defined notation is valid. The discussion highlights the importance of clarity in mathematical communication.

PREREQUISITES
  • Understanding of basic calculus concepts
  • Familiarity with function notation
  • Knowledge of the difference between average and instantaneous rates of change
  • Ability to interpret mathematical symbols and expressions
NEXT STEPS
  • Research the application of average rate of change in real-world scenarios
  • Explore the concept of instantaneous rate of change and its relation to derivatives
  • Study different notations used in calculus and their contexts
  • Learn about defining custom notation in mathematical writing
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Is this the correct symbol to use for average rate of change:
[math]\overline{\triangle}=\dfrac{f(b)-f(a)}{b-a} [/math]
 
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The correct notation for average rate of change is:
$$\frac{\Delta f}{\Delta x} = \frac{f(b)-f(a)}{b-a}$$
 
I would say that Greg's example is the "standard" or "usual" symbol for rate of change and that there is no "correct" symbol for anything! As long as you define your notation, there is no "incorrect" notation.
 

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