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. $f ( x ) = \frac { 1 } { x + 4 } , \quad ( - 3,1 )$
A) $\begin{array} { l }
m = \frac { 1 } { ( x + 4 ) ^ { 2 } } \
\text { At } ( - 3,1 ) , m = 1
\end{array}$
B) $\begin{array} { l }
m = - \frac { 1 } { ( x + 4 ) ^ { 2 } } \
\text { At } ( - 3,1 ) , m = 1
\end{array}$
C) $\begin{array} { l }
m = \frac { 1 } { ( x + 4 ) ^ { 2 } } \
\text { At } ( - 3,1 ) , m = - 1
\end{array}$
D) $\begin{array} { l }
m = - \frac { 1 } { ( x + 4 ) } \
\text { At } ( - 3,1 ) , m = - 1
\end{array}$
E) $\begin{array} { l }
m = - \frac { 1 } { ( x + 4 ) ^ { 2 } } \
\text { At } ( - 3,1 ) , m = - 1
\end{array}$

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.   $f ( x ) = \frac { 1 } { x + 4 } , \quad ( - 3,1 )$  
A) $\begin{array} { l } 
m = \frac { 1 } { ( x + 4 ) ^ { 2 } } \
\text { At } ( - 3,1 ) , m = 1
\end{array}$  
B) $\begin{array} { l } 
m = - \frac { 1 } { ( x + 4 ) ^ { 2 } } \
\text { At } ( - 3,1 ) , m = 1
\end{array}$  
C) $\begin{array} { l } 
m = \frac { 1 } { ( x + 4 ) ^ { 2 } } \
\text { At } ( - 3,1 ) , m = - 1
\end{array}$ 
D) $\begin{array} { l } 
m = - \frac { 1 } { ( x + 4 ) } \
\text { At } ( - 3,1 ) , m = - 1
\end{array}$  
E) $\begin{array} { l } 
m = - \frac { 1 } { ( x + 4 ) ^ { 2 } } \
\text { At } ( - 3,1 ) , m = - 1
\end{array}$

Quizplus · Accepted Answer

The slope of the graph of $f(x) = \frac{1}{x+4}$ is found by differentiating $f(x)$ with respect to $x$, which gives $f'(x) = -\frac{1}{(x+4)^2}$. At the point $(-3,1)$, substituting $x = -3$ into the derivative gives $m = -\frac{1}{(-3+4)^2} = -1$.

Find a Formula for the Slope of the Graph Of f