Respuesta :

akaleti47
f(1)=0,f(5)=120

{average rate of change of f(x) over the interval [1, 5] } = [f(5)-f(1)]/(5-1)=120/4=30

Answer:

The average rate of change in the interval [1,5] is 30.

Step-by-step explanation:

The function is given by [tex]f(x)=x^3-x[/tex]

Then, we have that,

[tex]f(5)=5^3-5\\\\f(5)=125-5\\\\f(5)=120[/tex]

Also, we have,

[tex]f(1)=1^3-1\\\\f(1)=1-1\\\\f(1)=0[/tex]

So, the average rate of change over the interval [1,5] will be,

[tex]Rate=\dfrac{f(5)-f(1)}{5-1}\\\\Rate=\dfrac{120-0}{4}\\\\Rate=\dfrac{120}{4}\\\\Rate=30[/tex]

Thus, the average rate of change in the interval [1,5] is 30.

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