Find the average rate of change of the function from $$x _ { 1 } \text { to } x _ { 2 }$$
-$f ( x ) = - 3 x ^ { 2 } - x$ from $x _ { 1 } = 5$ to $x _ { 2 } = 6$
A) $- 34$
B) $- 2$
C) $\frac { 1 } { 2 }$
D) $- \frac { 1 } { 6 }$

Question

Quizplus · Accepted Answer

The average rate of change of a function $f(x)$ from $x_1$ to $x_2$ is given by $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$. For $f(x) = -3x^2 - x$, $f(5) = -3(5)^2 - 5 = -75 - 5 = -80$ and $f(6) = -3(6)^2 - 6 = -108 - 6 = -114$. Thus, the average rate of change from $x_1 = 5$ to $x_2 = 6$ is $\frac{-114 - (-80)}{6 - 5} = \frac{-34}{1} = -34$.

Find the Average Rate of Change of the Function From x