Question

given the function $h(x)=x^{2}+6x + 3$, determine the average rate of change of the function over the interval $-5leq xleq2$. answer attempt 1 out of 2

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 $\frac{h(b)-h(a)}{b - a}$. Here, $a=-5$ and $b = 2$.

Step2: Calculate $h(-5)$

Substitute $x=-5$ into $h(x)=x^{2}+6x + 3$.
$h(-5)=(-5)^{2}+6\times(-5)+3=25-30 + 3=-2$.

Step3: Calculate $h(2)$

Substitute $x = 2$ into $h(x)=x^{2}+6x + 3$.
$h(2)=2^{2}+6\times2+3=4 + 12+3=19$.

Step4: Calculate the average rate of change

Use the formula $\frac{h(2)-h(-5)}{2-(-5)}$.
$\frac{19-(-2)}{2 + 5}=\frac{19 + 2}{7}=\frac{21}{7}=3$.

Answer:

$3$