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

Average rate of change is 2

Explanation:

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

`\displaystyle (f(b)-f(a))/(b-a)\\\\=\displaystyle (f(1)-f(-1))/(1-(-1))\\\\=((2(1)-11)-(2(-1)-11))/(1+1)\\ \\=((2-11)-(-2-11))/(2)\\ \\=(-9-(-13))/(2)\\ \\=(-9+13)/(2)\\ \\=(4)/(2)\\ \\=2`

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