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Given f(x)= 1/x+6, find the average rate of change of f(x) on the interval [8,8+h]. Your answer will be an expression involving h

Sagot :

Function:

[tex]f(x)=\frac{1}{x+6}[/tex]

Interval: [ 8, 8+h ]

Average rate of change:

[tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex]

where a = 8 and b = 8 + h...

[tex]\begin{gathered} f(b)=\frac{1}{b+6} \\ f(8+h)=\frac{1}{8+h+6}=\frac{1}{h+14} \\ f(8+h)=\frac{1}{h+14} \end{gathered}[/tex][tex]\begin{gathered} f(a)=\frac{1}{a+6} \\ f(8)=\frac{1}{8+6}=\frac{1}{14} \end{gathered}[/tex]

Then:

[tex]\begin{gathered} A(x)=\frac{\frac{1}{h+14}-\frac{1}{14}}{8+h-8}=\frac{\frac{1}{h+14}-\frac{1}{14}}{h}=-\frac{1}{14\cdot(h+14)} \\ A(x)=-\frac{1}{14h+196} \end{gathered}[/tex]

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