Answer :
Answer:
The average rate of change of f(x) over the interval −1 ≤ x ≤ 1 is -1.
Step-by-step explanation:
The average rate of change of a function is:
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
The function is:
[tex]f(x)=x^{2}-x-1[/tex]
The interval is, -1 ≤ x ≤ 1.
Compute the average rate of change as follows:
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
[tex]=\frac{((1)^{2}-1-1)-((-1)^{2}-(-1)-1)}{1-(-1)}\\\\=\frac{-1-1}{2}\\\\=-1[/tex]
Thus, the average rate of change of f(x) over the interval −1 ≤ x ≤ 1 is -1.