find the average rate of change of ( k(x)=\frac{-16}{x + 12} ) over the interval ( -11,-10 ).\nwrite your…

find the average rate of change of ( k(x)=\frac{-16}{x + 12} ) over the interval ( -11,-10 ).\nwrite your answer as an integer, fraction, or decimal rounded to the nearest tenth.\nsimplify any fractions.

find the average rate of change of ( k(x)=\frac{-16}{x + 12} ) over the interval ( -11,-10 ).\nwrite your answer as an integer, fraction, or decimal rounded to the nearest tenth.\nsimplify any fractions.

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = k(x)) over the interval ([a,b]) is (\frac{k(b)-k(a)}{b - a}). Here, (a=-11), (b = - 10).

Step2: Find (k(-11)) and (k(-10))

For (k(x)=\frac{-16}{x + 12}), when (x=-11), (k(-11)=\frac{-16}{-11 + 12}=\frac{-16}{1}=-16). When (x=-10), (k(-10)=\frac{-16}{-10 + 12}=\frac{-16}{2}=-8).

Step3: Calculate the average rate of change

Substitute into the formula: (\frac{k(-10)-k(-11)}{-10-(-11)}=\frac{-8-(-16)}{-10 + 11}). Simplify the numerator: (-8 + 16=8), and the denominator: (-10 + 11 = 1).

Answer:

(8)