Question

For the function f(x) = 2x - 11, what is the average rate of change over the interval -1 ≤ x ≤ 1? average rate of change:​

Answer 1

Answer:

Average rate of change is 2

Step-by-step explanation:

If a function $f(x)$ is continuous over the interval $[a,b]$, then the average rate of change over that interval is $\displaystyle \frac{f(b)-f(a)}{b-a}$:

$\displaystyle \frac{f(b)-f(a)}{b-a}\\\\=\displaystyle \frac{f(1)-f(-1)}{1-(-1)}\\\\=\frac{(2(1)-11)-(2(-1)-11)}{1+1}\\ \\=\frac{(2-11)-(-2-11)}{2}\\ \\=\frac{-9-(-13)}{2}\\ \\=\frac{-9+13}{2}\\ \\=\frac{4}{2}\\ \\=2$

Thus, the average rate of  change over the interval $[-1,1]$ for the function $f(x)=2x-11$ is 2.