given the function defined in the table below, find the average rate of change, in simplest form, of the…

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $5 \\leq x \\leq 7$.

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $5 \\leq x \\leq 7$.

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 5) and (b=7).

Step2: Identify (f(a)) and (f(b))

From the table, when (x = 5), (f(5)=16); when (x = 7), (f(7)=64).

Step3: Substitute into the formula

Substitute (a = 5), (b = 7), (f(a)=16), and (f(b)=64) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{64 - 16}{7-5}).

Step4: Simplify the expression

First, calculate the numerator: (64-16=48). Then calculate the denominator: (7 - 5=2). So, (\frac{48}{2}=24).

Answer:

(24)