The average rate of change of the given function is 10π.
Given function
a = πx^2
Where a is the area of a circle with radius x
The radius changes from x = 4 to x = 6.
Calculating the average rate of change of function:
The method of finding the average rate between the function value over a certain interval is called the average rate of change.
The formula is given by :
Average = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Where f(a) and f(b) are the function value over the limit a and b.
Average = [tex]\frac{f(6)-f(4)}{6-4}[/tex]
= [tex]\frac{\pi (6)^{2} -\pi (4)^{2} }{6-4}[/tex]
= [tex]\frac{\pi (36-16)}{2}[/tex]
= [tex]\frac{20\pi }{2}[/tex]
= 10π
The average rate of change of the given function is 10π.
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