Question

question
given the function $h(x) = x^2 + 5x - 1$, determine the average rate of change of the function over the interval $-6 \leq x \leq 0$.
answer attempt 1 out of 3
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Explanation:

Step1: Define average rate of change formula

The average rate of change of a function $h(x)$ over $[a,b]$ is $\frac{h(b)-h(a)}{b-a}$.
Here, $a=-6$, $b=0$.

Step2: Calculate $h(0)$

Substitute $x=0$ into $h(x)$:
$h(0) = 0^2 + 5(0) - 1 = -1$

Step3: Calculate $h(-6)$

Substitute $x=-6$ into $h(x)$:
$h(-6) = (-6)^2 + 5(-6) - 1 = 36 - 30 - 1 = 5$

Step4: Compute average rate of change

Substitute values into the formula:
$\frac{h(0)-h(-6)}{0-(-6)} = \frac{-1 - 5}{0 + 6} = \frac{-6}{6} = -1$

Answer:

$-1$