Answer:
Hence, the average rate of change is:
[tex]\dfrac{97}{12}[/tex]
Step-by-step explanation:
We are asked to calculate the average value of the function:
[tex]f(x)=x^2-\dfrac{1}{x}-4[/tex] in 2 ≤ x ≤ 6
The average rate of change of the function f(x) in the interval 2 ≤ x ≤ 6 is given as:
[tex]\dfrac{f(6)-f(2)}{6-2}\\\\=\dfrac{f(6)-f(2)}{4}[/tex]
Now,
[tex]f(6)=36-\dfrac{1}{6}-4\\\\f(6)=32-\dfrac{1}{6}\\\\f(6)=\dfrac{191}{6}[/tex]
[tex]f(2)=4-\dfrac{1}{2}-4\\\\\\f(2)=-\dfrac{1}{2}[/tex]
Hence, the average rate of change is:
[tex]\dfrac{\dfrac{191}{6}-\dfrac{-1}{2}}{4}\\\\=\dfrac{194}{6\times 4}\\\\=\dfrac{97}{12}[/tex]
Hence, the average rate of change is:
[tex]\dfrac{97}{12}[/tex]
