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. $f ( x ) = \sqrt { x - 3 } , \quad ( 52,7 )$
A) $\begin{array} { l }
m = \frac { 1 } { 2 \sqrt { x - 3 } } \
\text { At } ( 52,7 ) , m = - \frac { 1 } { 14 }
\end{array}$
B) $\begin{array} { l }
m = \frac { 1 } { 2 \sqrt { x - 3 } } \
\operatorname { At } ( 52,7 ) , m = \frac { 1 } { 14 }
\end{array}$
C) $\begin{array} { l }
m = \frac { 1 } { \sqrt { x - 3 } } \
\operatorname { At } ( 52,7 ) , m = \frac { 1 } { 14 }
\end{array}$
D) $\begin{array} { l }
m = - \frac { 1 } { 2 \sqrt { x - 3 } } \
\operatorname { At } ( 52,7 ) , m = \frac { 1 } { 14 }
\end{array}$
E) $\begin{array} { l }
m = - \frac { 1 } { 2 \sqrt { x - 3 } } \
\text { At } ( 52,7 ) , m = - \frac { 1 } { 14 }
\end{array}$

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.  $f ( x ) = \sqrt { x - 3 } , \quad ( 52,7 )$  
A) $\begin{array} { l } 
m = \frac { 1 } { 2 \sqrt { x - 3 } } \
\text { At } ( 52,7 ) , m = - \frac { 1 } { 14 }
\end{array}$  
B) $\begin{array} { l } 
m = \frac { 1 } { 2 \sqrt { x - 3 } } \
\operatorname { At } ( 52,7 ) , m = \frac { 1 } { 14 }
\end{array}$  
C) $\begin{array} { l } 
m = \frac { 1 } { \sqrt { x - 3 } } \
\operatorname { At } ( 52,7 ) , m = \frac { 1 } { 14 }
\end{array}$  
D) $\begin{array} { l } 
m = - \frac { 1 } { 2 \sqrt { x - 3 } } \
\operatorname { At } ( 52,7 ) , m = \frac { 1 } { 14 }
\end{array}$  
E) $\begin{array} { l } 
m = - \frac { 1 } { 2 \sqrt { x - 3 } } \
\text { At } ( 52,7 ) , m = - \frac { 1 } { 14 }
\end{array}$

Quizplus · Accepted Answer

The derivative of $f(x) = \sqrt{x - 3}$ is $f'(x) = \frac{1}{2\sqrt{x - 3}}$, which gives the slope of the tangent to the graph at any point $x$. At the point $(52, 7)$, substituting $x = 52$ into the derivative formula gives $m = \frac{1}{2\sqrt{52 - 3}} = \frac{1}{2\sqrt{49}} = \frac{1}{2 \cdot 7} = \frac{1}{14}$.

Find a Formula for the Slope of the Graph Of f