Question

Consider f(x)=2|x|

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

As we know that the average rate of change of f(x) in the closed

interval [a, b] is

$\frac{f\left(b\right)-f\left(a\right)}{b-a}$

Given the interval [a, b] = [0, 4]

as

$f(x)=2|x|$

$f(b)=f(2)=2\cdot \:4$       ∵  $\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0$

      $= 8$

   

$f(x)=2|x|$

$f(a)=f(0)=2\cdot \:0$       ∵  $\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0$

       $= 0$

so the average rate of change  :

$\frac{f\left(b\right)-f\left(a\right)}{b-a}=\frac{8-0}{4-0}$

              $=\frac{8}{4}$

               $= 2$

We know that a rate of change basically indicates how an output quantity changes relative to the change in the input quantity. Here, it is clear the value of y increase with the increase of input.