MHB Average Rate Of Change Formula

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The average rate of change formula is expressed as \(\frac{\Delta f}{\Delta x} = \frac{f(b)-f(a)}{b-a}\). There is debate over the correct symbol to use, with some arguing that the notation \(\overline{\triangle}\) is also acceptable. The consensus suggests that while there is a standard symbol, any notation can be valid if properly defined. Ultimately, the emphasis is on clarity and consistency in notation rather than strict adherence to one symbol. Defining your notation is key to effective communication in mathematical contexts.
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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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