Find the average rate of change for the function between the given values.
-$f ( x ) = \sqrt { 2 x - 1 } ;$ from 1 to 5
A) $\frac { 1 } { 2 }$
B) $- 2$
C) $- \frac { 1 } { 6 }$
D) $- 28$

Question

Quizplus · Accepted Answer

The average rate of change of a function $f(x)$ between two points $x = a$ and $x = b$ is given by $\frac{f(b) - f(a)}{b - a}$. For $f(x) = \sqrt{2x - 1}$, from $x = 1$ to $x = 5$, we calculate $f(1) = \sqrt{2(1) - 1} = \sqrt{1} = 1$ and $f(5) = \sqrt{2(5) - 1} = \sqrt{9} = 3$. Thus, the average rate of change is $\frac{3 - 1}{5 - 1} = \frac{2}{4} = \frac{1}{2}$.

Find the Average Rate of Change for the Function Between f(x)=2x−1;f ( x ) = \sqrt { 2 x - 1 } ;f(x)=2x−1​;

Find the Average Rate of Change for the Function Between $f ( x ) = \sqrt { 2 x - 1 } ;$