Find a formula for the slope of the graph of $f$ at the point $( x , f ( x ) )$ .Then use it to find the slope at the given point. $f ( x ) = \sqrt { x - 4 } , \quad ( 8,2 )$
A) $\begin{array} { l }
m = \frac { 1 } { \sqrt { x - 4 } } \
A t ( 8,2 ) , m = \frac { 1 } { 4 }
\end{array}$
B) $\begin{array} { l }
m = - \frac { 1 } { 2 \sqrt { x - 4 } } \
\text { At } ( 8,2 ) , m = \frac { 1 } { 4 }
\end{array}$
C) $\begin{array} { l }
m = \frac { 1 } { 2 \sqrt { x - 4 } } \
A t ( 8,2 ) , m = \frac { 1 } { 4 }
\end{array}$
D) $\begin{array} { l }
m = \frac { 1 } { 2 \sqrt { x - 4 } } \
A t ( 8,2 ) , m = - \frac { 1 } { 4 }
\end{array}$
E) $\begin{array} { l }
m = - \frac { 1 } { 2 \sqrt { x - 4 } } \
\text { At } ( 8,2 ) , m = - \frac { 1 } { 4 }
\end{array}$

Question

Find a formula for the slope of the graph of $f$ at the point $( x , f ( x ) )$ .Then use it to find the slope at the given point.   $f ( x ) = \sqrt { x - 4 } , \quad ( 8,2 )$  
A) $\begin{array} { l } 
m = \frac { 1 } { \sqrt { x - 4 } } \
A t ( 8,2 ) , m = \frac { 1 } { 4 }
\end{array}$  
B) $\begin{array} { l } 
m = - \frac { 1 } { 2 \sqrt { x - 4 } } \
\text { At } ( 8,2 ) , m = \frac { 1 } { 4 }
\end{array}$  
C) $\begin{array} { l } 
m = \frac { 1 } { 2 \sqrt { x - 4 } } \
A t ( 8,2 ) , m = \frac { 1 } { 4 }
\end{array}$  
D) $\begin{array} { l } 
m = \frac { 1 } { 2 \sqrt { x - 4 } } \
A t ( 8,2 ) , m = - \frac { 1 } { 4 }
\end{array}$  
E) $\begin{array} { l } 
m = - \frac { 1 } { 2 \sqrt { x - 4 } } \
\text { At } ( 8,2 ) , m = - \frac { 1 } { 4 }
\end{array}$

Quizplus · Accepted Answer

The derivative of $f(x) = \sqrt{x - 4}$ is $f'(x) = \frac{1}{2\sqrt{x - 4}}$. At the point (8,2), the slope is $m = \frac{1}{2\sqrt{8 - 4}} = \frac{1}{4}$.

Find a Formula for the Slope of the Graph Of f