Question

Calculate the average rate of change of f(x) = x2 - 1 x - 4 for 2 ≤ x ≤ 6.

Answer 1

Answer:

Hence, the average rate of change is:

$\dfrac{97}{12}$

Step-by-step explanation:

We are asked to calculate the average value of the function:

$f(x)=x^2-\dfrac{1}{x}-4$ in 2 ≤ x ≤ 6

The average rate of change of the function f(x) in the interval 2 ≤ x ≤ 6  is given as:

$\dfrac{f(6)-f(2)}{6-2}\\\\=\dfrac{f(6)-f(2)}{4}$

Now,

$f(6)=36-\dfrac{1}{6}-4\\\\f(6)=32-\dfrac{1}{6}\\\\f(6)=\dfrac{191}{6}$

$f(2)=4-\dfrac{1}{2}-4\\\\\\f(2)=-\dfrac{1}{2}$

Hence, the average rate of change is:

$\dfrac{\dfrac{191}{6}-\dfrac{-1}{2}}{4}\\\\=\dfrac{194}{6\times 4}\\\\=\dfrac{97}{12}$

Hence, the average rate of change is:

$\dfrac{97}{12}$

Answer 2

Answer:

Step-by-step explanation: