find the average rate of change of ( h(x)=-sqrt{x + 20} ) over the interval ( -2,9 ). write your answer as…

Explanation:

Step1: Recall the formula for average rate of change

The formula for 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=-2), (b = 8), and (h(x)=-\sqrt{x + 20}).

Step2: Calculate (h(a)) and (h(b))

• When (x=a=-2), (h(-2)=-\sqrt{-2 + 20}=-\sqrt{18}=-3\sqrt{2}).
• When (x = b = 8), (h(8)=-\sqrt{8+20}=-\sqrt{28}=-2\sqrt{7}).

Step3: Substitute into the average - rate - of - change formula

(\frac{h(8)-h(-2)}{8-(-2)}=\frac{-2\sqrt{7}-(-3\sqrt{2})}{8 + 2}=\frac{-2\sqrt{7}+3\sqrt{2}}{10}\approx\frac{-2\times2.646+3\times1.414}{10}=\frac{-5.292 + 4.242}{10}=\frac{-1.05}{10}=-0.105)

Answer:

(-0.105)