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.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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