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

Question

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

Quizplus · Accepted Answer

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

Find the Average Rate of Change for the Function Between f(x)=−3x2−x; from 5 to 6f ( x ) = - 3 x ^ { 2 } - x ; \text { from } 5 \text { to } 6f(x)=−3x2−x; from 5 to 6

Find the Average Rate of Change for the Function Between $f ( x ) = - 3 x ^ { 2 } - x ; \text { from } 5 \text { to } 6$