question given the function $h(x)=-x^{2}-2x + 3$, determine the average rate of change of the function over…

question given the function $h(x)=-x^{2}-2x + 3$, determine the average rate of change of the function over the interval $-6leq xleq5$. answer attempt 2 out of 2

question given the function $h(x)=-x^{2}-2x + 3$, determine the average rate of change of the function over the interval $-6leq xleq5$. answer attempt 2 out of 2

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(x)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$, where $a=-6$ and $b = 5$.

Step2: Calculate $h(-6)$

Substitute $x=-6$ into $h(x)=-x^{2}-2x + 3$. $h(-6)=-(-6)^{2}-2\times(-6)+3=-36 + 12+3=-21$.

Step3: Calculate $h(5)$

Substitute $x = 5$ into $h(x)=-x^{2}-2x + 3$. $h(5)=-5^{2}-2\times5+3=-25-10 + 3=-32$.

Step4: Calculate the average rate of change

$\frac{h(5)-h(-6)}{5-(-6)}=\frac{-32-(-21)}{5 + 6}=\frac{-32 + 21}{11}=\frac{-11}{11}=-1$.

Answer:

$-1$