Answer:
The average rate of change for the function between the given interval is;
[tex]-12[/tex]Explanation:
The average rate of change for the given function;
[tex]f(x)=3x^2-5[/tex]Between the interval;
[tex]-3\leq x\leq-1[/tex]can be calculated as;
[tex]\Delta f(x)=\frac{f(-1)-f(-3)}{-1-(-3)}=\frac{f(-1)-f(-3)}{2}[/tex]The value of f(x) at x=-1 and -3 are;
[tex]\begin{gathered} f(-1)=3(-1)^2-5=-2 \\ f(-3)=3(-3)^2-5=27-5=22 \end{gathered}[/tex]So;
[tex]\begin{gathered} \Delta f(x)=\frac{f(-1)-f(-3)}{2}=\frac{-2-22}{2}=-\frac{24}{2} \\ \Delta f(x)=-12 \end{gathered}[/tex]Therefore, the average rate of change for the function between the given interval is;
[tex]-12[/tex]