Question

Given the function
h(x) = -x² − x + 5,
determine the average rate of change of the function over the interval -6 ≤ x ≤ 2.

Answer 1

Answer:

3

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by the formula:

$\boxed{\dfrac{f(b)-f(a)}{b-a}}$

Given interval:

-6 ≤ x ≤ 2

Therefore:

• a = -6
• b = 2

Given function:

$h(x) = -x^2 - x + 5$

Therefore:

$\implies h(-6)=-(-6)^2-(-6)+5=-25$

$\implies h(2)=-(2)^2-(2)+5=-1$

Substitute the found values into the formula:

$\begin{aligned}\implies \dfrac{h(b)-h(a)}{b-a} & = \dfrac{h(2)-h(-6)}{2-(-6)}\\\\ & =\dfrac{-1-(-25)}{2+6}\\\\& = \dfrac{24}{8}\\\\& = 3\end{aligned}$

Therefore, the average rate of change over the given interval is 3.

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