Respuesta :

absor201

Answer:

4.75

Step-by-step 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 ..

lublana

Answer:

Average rate of change =4.75.

Step-by-step explanation:

Given function is [tex]f\left(x\right)=\frac{x^2-1}{x-4}[/tex].

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

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

[tex]ARC=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]

[tex]ARC=\frac{f\left(6\right)-f\left(2\right)}{6-2}[/tex]

[tex]ARC=\frac{\frac{6^2-1}{6-4}-\frac{2^2-1}{2-4}}{4}[/tex]

[tex]ARC=\frac{\frac{36-1}{6-4}-\frac{4-1}{2-4}}{4}[/tex]

[tex]ARC=\frac{17.5-\left(-1.5\right)}{4}[/tex]

[tex]ARC=\frac{19}{4}[/tex]

[tex]ARC=4.75[/tex]

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

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