Question

Caculaye the average rate of change of f(x)=x^2-1/x-4 for 2<=x<=6​

Answer 1

Average rate of change =4.75.

Explanation:

Given function is
`f\left(x\right)=(x^2-1)/(x-4)`.

Now we need to find the average rate of change of f(x) for
`2\le x\le6`.

So plug these values into average rate of change (ARC) formula.

`ARC=(f\left(b\right)-f\left(a\right))/(b-a)`

`ARC=(f\left(6\right)-f\left(2\right))/(6-2)`

`ARC=((6^2-1)/(6-4)-(2^2-1)/(2-4))/(4)`

`ARC=((36-1)/(6-4)-(4-1)/(2-4))/(4)`

`ARC=(17.5-\left(-1.5\right))/(4)`

`ARC=(19)/(4)`

`ARC=4.75`

So the final answer is average rate of change =4.75.

Answer 2

4.75

Explanation:

Given

f(x)= (x^2-1)/(x-4)

The average rate of change for the interval a≤x≤b is given by:

Rate of change= (f(b)-f(a))/(b-a)

In our question,

a=2

and

b=6

So,

f(2)= ((2)^2-1)/(2-4)

=(4-1)/(-2)

= -3/2

And

f(6)= ((6)^2-1)/(6-4)

=(36-1)/2

= 35/2

Rate of change= ( 35/2-(-3/2))/(6-2)

=(35/2+3/2)/(6-2)

= ((35+3)/2)/4

=(38/2)/4

=19/4

=4.75

The average rate of change is 4.75 ..