question given the function f(x)=x² + x - 4, determine the average rate of change of the function over the…

question given the function f(x)=x² + x - 4, determine the average rate of change of the function over the interval -6 ≤ x ≤ 4.

question given the function f(x)=x² + x - 4, determine the average rate of change of the function over the interval -6 ≤ x ≤ 4.

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-6$, $b = 4$, and $f(x)=x^{2}+x - 4$.

Step2: Calculate $f(a)$

Substitute $x=-6$ into $f(x)$: $f(-6)=(-6)^{2}+(-6)-4=36 - 6-4=26$.

Step3: Calculate $f(b)$

Substitute $x = 4$ into $f(x)$: $f(4)=4^{2}+4-4=16$.

Step4: Calculate the average rate of change

$\frac{f(4)-f(-6)}{4-(-6)}=\frac{16 - 26}{4 + 6}=\frac{-10}{10}=-1$.

Answer:

$-1$