Question

Find the average rate of change of g ( x ) = 3 x^3 − 4 from x = − 4 to x = 1 .

Answer 1

Solution:

The average rate of change is calculated using;

$\begin{gathered} \frac{g(b)-g(a)}{b-a} \\ Where; \\ a=-4,b=1 \end{gathered}$

Then;

$\begin{gathered} g(x)=3x^3-4 \\ \\ g(-4)=3(-4)^3-4 \\ \\ g(-4)=3(-64)-4 \\ \\ g(-4)=-192-4 \\ \\ g(-4)=-196 \\ \\ g(1)=3(1)^3-4 \\ \\ g(1)=3(1)-4 \\ \\ g(1)=3-4 \\ \\ g(1)=-1 \end{gathered}$

Thus, the average rate of change is;

$\begin{gathered} =\frac{-1-(-196)}{1-(-4)} \\ \\ =\frac{195}{5} \\ \\ =39 \end{gathered}$

ANSWER: 39