1 Answer

Sasidharan · Answer 1 · 2022-12-16T17:56:21+0000

Given:

Consider the given function is:

f(x)=x^2-8x+13

To find:

The average rate of change of the function over the interval
$-1\leq x\leq 6$ .

Solution:

The average rate of change of the function f(x) over the interval [a,b] is:

m=(f(x_2)-f(x_1))/(x_2-x_1)

We have,

f(x)=x^2-8x+13

At
x=-1 ,

f(-1)=(-1)^2-8(-1)+13

f(-1)=1+8+13

f(-1)=22

At
x=6 ,

f(6)=(6)^2-8(6)+13

f(6)=36-48+13

f(6)=1

Now, the average rate of change of the function f(x) over the interval
$-1\leq x\leq 6$ is:

m=(f(6)-f(-1))/(6-(-1))

m=(1-22)/(7)

m=(-21)/(7)

m=-3

Therefore, the average rate of change of the function f(x) over the interval
$-1\leq x\leq 6$ is -3.

Please log in or register to add a comment.