find the average rate of change of the function f(x) = √x from x₁ = 9 to x₂ = 49.\nthe average rate of…

find the average rate of change of the function f(x) = √x from x₁ = 9 to x₂ = 49.\nthe average rate of change is □. (simplify your answer.)

find the average rate of change of the function f(x) = √x from x₁ = 9 to x₂ = 49.\nthe average rate of change is □. (simplify your answer.)

Answer

Explanation:

Step1: Find f(x1) and f(x2)

Given (f(x)=\sqrt{x}), when (x_1 = 9), (f(x_1)=\sqrt{9}=3); when (x_2 = 49), (f(x_2)=\sqrt{49}=7).

Step2: Use average - rate - of - change formula

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}). Substitute (f(x_1)=3), (f(x_2)=7), (x_1 = 9) and (x_2 = 49) into the formula: (\frac{7 - 3}{49-9}=\frac{4}{40}=\frac{1}{10}).

Answer:

(\frac{1}{10})