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. $f ( x ) = \sqrt { x - 1 } , \quad ( 17,4 )$
A) $\begin{array} { l }
m = \frac { 1 } { \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = \frac { 1 } { 8 }
\end{array}$
B) $\begin{array} { l }
m = \frac { 1 } { 2 \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = \frac { 1 } { 8 }
\end{array}$
C) $\begin{array} { l }
m = \frac { 1 } { 2 \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = - \frac { 1 } { 8 }
\end{array}$
D) $\begin{array} { l }
m = - \frac { 1 } { 2 \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = \frac { 1 } { 8 }
\end{array}$
E) $\begin{array} { l }
m = - \frac { 1 } { 2 \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = - \frac { 1 } { 8 }
\end{array}$

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.   $f ( x ) = \sqrt { x - 1 } , \quad ( 17,4 )$  
A) $\begin{array} { l } 
m = \frac { 1 } { \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = \frac { 1 } { 8 }
\end{array}$  
B) $\begin{array} { l } 
m = \frac { 1 } { 2 \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = \frac { 1 } { 8 }
\end{array}$  
C)  $\begin{array} { l } 
m = \frac { 1 } { 2 \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = - \frac { 1 } { 8 }
\end{array}$  
D) $\begin{array} { l } 
m = - \frac { 1 } { 2 \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = \frac { 1 } { 8 }
\end{array}$  
E)  $\begin{array} { l } 
m = - \frac { 1 } { 2 \sqrt { x - 1 } } \
\text { At } ( 17,4 ) , m = - \frac { 1 } { 8 }
\end{array}$

Quizplus · Accepted Answer

The derivative of $f(x) = \sqrt{x - 1}$ is $f'(x) = \frac{1}{2\sqrt{x - 1}}$, which gives the slope of the graph at any point $x$. At the point $(17, 4)$, substituting $x = 17$ into the derivative formula gives $m = \frac{1}{2\sqrt{17 - 1}} = \frac{1}{2\sqrt{16}} = \frac{1}{2 \cdot 4} = \frac{1}{8}$.

Find a Formula for the Slope of the Graph Of f