The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]
Given,
The function f(x) =[tex]8x^{2} -5[/tex]
The intervals = [4,b]
The average rate of change = [tex]\frac{f(a)-f(b)}{a-b}[/tex]
Where a and b are the interval
f(4)= [tex]8(4)^{2}-5[/tex]
=123
f(b)= [tex]8b^{2}-5[/tex]
The average rate of change = [tex]\frac{123-(8b^{2}-5) }{4-b}[/tex]
[tex]=\frac{123-8b^{2}+5 }{4-b} \\=\frac{128-8b^{2} }{4-b}[/tex]
Hence, The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]
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