Question

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

A) - 12/97
B) - 97/12
C) 12/97
D) 97/12

Answer 1

Explanation:

Answer 2

Hence, the average rate of change is:

`(97)/(12)`

Explanation:

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

`f(x)=x^2-(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:

`(f(6)-f(2))/(6-2)\\\\=(f(6)-f(2))/(4)`

Now,

`f(6)=36-(1)/(6)-4\\\\f(6)=32-(1)/(6)\\\\f(6)=(191)/(6)`

`f(2)=4-(1)/(2)-4\\\\\\f(2)=-(1)/(2)`

Hence, the average rate of change is:

`((191)/(6)-(-1)/(2))/(4)\\\\=(194)/(6* 4)\\\\=(97)/(12)`

Hence, the average rate of change is:

`(97)/(12)`