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

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

Quizplus · Accepted Answer

The derivative of $f(x) = 3 - x^2$ is $f'(x) = -2x$, which gives the slope of the graph at any point $x$. Substituting $x = -1$ into $f'(x) = -2x$ gives $m = -2(-1) = 2$.

Find a Formula for the Slope of the Graph Of f