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. $f ( x ) = \frac { 1 } { x + 8 } , \quad \left( 0 , \frac { 1 } { 8 } \right)$
A) $\begin{array} { l }
m = \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = - \frac { 1 } { 64 }
\end{array}$
B) $\begin{array} { l }
m = - \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = \frac { 1 } { 64 }
\end{array}$
C) $\begin{array} { l }
m = - \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = - \frac { 1 } { 8 }
\end{array}$
D) $\begin{array} { l }
m = - \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = - \frac { 1 } { 64 }
\end{array}$
E) $\begin{array} { l }
m = \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = \frac { 1 } { 64 }
\end{array}$

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.   $f ( x ) = \frac { 1 } { x + 8 } , \quad \left( 0 , \frac { 1 } { 8 } \right)$  
A)  $\begin{array} { l } 
m = \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = - \frac { 1 } { 64 }
\end{array}$   
B) $\begin{array} { l } 
m = - \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = \frac { 1 } { 64 }
\end{array}$  
C)  $\begin{array} { l } 
m = - \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = - \frac { 1 } { 8 }
\end{array}$  
D) $\begin{array} { l } 
m = - \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = - \frac { 1 } { 64 }
\end{array}$  
E) $\begin{array} { l } 
m = \frac { 1 } { ( x + 8 ) ^ { 2 } } \
\text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = \frac { 1 } { 64 }
\end{array}$

Quizplus · Accepted Answer

The slope of the graph of $f(x) = \frac{1}{x+8}$ at any point is found by differentiating $f(x)$ with respect to $x$, which gives $f'(x) = -\frac{1}{(x+8)^2}$. Substituting $x = 0$ into $f'(x)$ gives the slope at the point $(0, \frac{1}{8})$ as $-\frac{1}{64}$.

Find a Formula for the Slope of the Graph Of f