Find the average rate of change of the function over the given interval.
-$y = - 3 x ^ { 2 } - x , [ 5,6 ]$
A) $\frac { 1 } { 2 }$
B) $- 2$
C) $- 34$
D) $= \frac { 1 } { 6 }$

Question

Quizplus · Accepted Answer

The average rate of change of a function $y = f(x)$ over an interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$. For the given function $y = -3x^2 - x$ over the interval $[5, 6]$, we first find $f(5) = -3(5)^2 - 5 = -75 - 5 = -80$ and $f(6) = -3(6)^2 - 6 = -108 - 6 = -114$. Then, 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 of the Function Over y=−3x2−x,[5,6]y = - 3 x ^ { 2 } - x , [ 5,6 ]y=−3x2−x,[5,6]

Find the Average Rate of Change of the Function Over $y = - 3 x ^ { 2 } - x , [ 5,6 ]$