The average rate of change in f(x) over (1,5) is -6.
Given function is:
[tex]f(x) =17-x^{2}[/tex]
[tex]f(5) = -8\\\\f(1) = 16[/tex]
What is the average rate of change in a function over an interval?
The average rate of change is a measure of how much the function changed per unit, on average, over that interval.
We know that
The average rate of change in f(x) over (a,b) is given by:
The average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
So, The average rate of change in f(x) over (1,5) = [tex]\frac{f(5)-f(1)}{5-1}[/tex]
The average rate of change in f(x) over (1,5) = [tex]\frac{-8-16}{5-1}[/tex]
The average rate of change in f(x) over (1,5) = -6.
Therefore, the average rate of change in f(x) over (1,5) is -6.
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