The average rate of change of f(x)= x³-9x in interval [1,6] is 34.
If f(x) is a function the [a,b] is interval then the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Given the function is f(x)= x³-9x and the interval is [1,6].
then first we have to find the value of f(1) and f(6).
So
f(1) = (1)³-9(1)
= 1-9
= -8
and
f(6) = (6)³-9(6)
= 216- 54
= 162
therefore average rate of change of f is
[tex]\frac{f(6)-f(1)}{6-1}= \frac{162+8}{6-1}[/tex]
= 170/5
= 34
Hence the average rate of change of f is 34.
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