Question

What is the average rate of change in f(x) over the interval [4,13]?

a. 1/3
b.4/13
c. 11/13
d.11/8

Answer 1

we know that

Average Rate of Change. is the change in the y-value divided by the change in the x-value for two distinct points on the graph

So

`A=((f(b)-f(a)))/((b-a))`

in this problem

`a=4\\ b=13\\ f(a)=f(4)=8\\ f(b)=f(13)=11`

substitute the values in the formula above

`A=((11-8))/((13-4)) \\ \\ A=(3)/(9)`

Divide by
`3` both numerator and denominator

`A=(1)/(3)`

therefore

the answer is

`(1)/(3)`