find the average rate of change of the function ( f(x)=sqrt{x} ) from ( x_{1}=49 ) to ( x_{2}=121 ).\nthe…

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = f(x)) from (x_1) to (x_2) is (\frac{f(x_2)-f(x_1)}{x_2 - x_1}).

Step2: Find (f(x_1)) and (f(x_2))

Given (f(x)=\sqrt{x}), (x_1 = 49) and (x_2=121). (f(x_1)=\sqrt{49}=7), (f(x_2)=\sqrt{121} = 11).

Step3: Substitute into the formula

(\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{11 - 7}{121-49}). Simplify the denominator: (121 - 49=72). So, (\frac{11 - 7}{121-49}=\frac{4}{72}). Simplify the fraction: (\frac{4\div4}{72\div4}=\frac{1}{18}).

Answer:

(\frac{1}{18})