Find the average rate of change of the function over the given interval.
-$y = x ^ { 2 } + 4 x , [ 4,7 ]$
A) 15
B) $\frac { 45 } { 7 }$
C) 11
D) $\frac { 77 } { 3 }$

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 $y = x^2 + 4x$ and interval $[4, 7]$, we first find $f(4) = 4^2 + 4(4) = 16 + 16 = 32$ and $f(7) = 7^2 + 4(7) = 49 + 28 = 77$. Then, the average rate of change is $\frac{77 - 32}{7 - 4} = \frac{45}{3} = 15$.

Find the Average Rate of Change of the Function Over y=x2+4x,[4,7]y = x ^ { 2 } + 4 x , [ 4,7 ]y=x2+4x,[4,7]

Find the Average Rate of Change of the Function Over $y = x ^ { 2 } + 4 x , [ 4,7 ]$