Home > Calculus > Average Rate of Change Over an Interval

What is the average rate of change formula for a function?

Answer 1

For a function #f(x)# the average rate of change between #x=x_1# and #x=x_2# is
#color(white)("XXXX")##(f(x_2)-f(x_1))/(x_2-x_1)#

(The above formula assumes that the function is continuous in the range #[x_1,x_2]#)

This is basically just a definition but you might think of "the average rate of change" as #color(white)("XXXX")#the amount by which the function changes #color(white)("XXXX")##color(white)("XXXX")#divided by #color(white)("XXXX")#the distance over which that change takes place

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Answer 2

Aurora Alvarado

The average rate of change formula for a function ( f(x) ) over the interval ([a, b]) is given by:

[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.