Solution:
The average rate of change is calculated using;
[tex]\begin{gathered} \frac{g(b)-g(a)}{b-a} \\ Where; \\ a=-4,b=1 \end{gathered}[/tex]
Then;
[tex]\begin{gathered} g(x)=3x^3-4 \\ \\ g(-4)=3(-4)^3-4 \\ \\ g(-4)=3(-64)-4 \\ \\ g(-4)=-192-4 \\ \\ g(-4)=-196 \\ \\ g(1)=3(1)^3-4 \\ \\ g(1)=3(1)-4 \\ \\ g(1)=3-4 \\ \\ g(1)=-1 \end{gathered}[/tex]
Thus, the average rate of change is;
[tex]\begin{gathered} =\frac{-1-(-196)}{1-(-4)} \\ \\ =\frac{195}{5} \\ \\ =39 \end{gathered}[/tex]
ANSWER: 39
