Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. $h ( x ) = \sqrt { x + 10 } , \quad ( - 1,3 )$
A) $m = - \frac { 1 } { 6 }$
B) $m = 9$
C) $m = \frac { 1 } { 6 }$
D) $m = - 3$
E) $m = 3$

Question

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result.   $h ( x ) = \sqrt { x + 10 } , \quad ( - 1,3 )$  
A) $m = - \frac { 1 } { 6 }$
B) $m = 9$
C) $m = \frac { 1 } { 6 }$
D) $m = - 3$
E) $m = 3$

Quizplus · Accepted Answer

The slope of the graph of the function at a given point can be found using the derivative of the function at that point. The derivative of $h(x) = \sqrt{x + 10}$ with respect to $x$ is $h'(x) = \frac{1}{2\sqrt{x + 10}}$. Plugging in the x-coordinate of the given point, $x = -1$, we get $h'(-1) = \frac{1}{2\sqrt{-1 + 10}} = \frac{1}{2\sqrt{9}} = \frac{1}{6}$. Therefore, the slope of the graph at the point $(-1, 3)$ is $\frac{1}{6}$.

Use the Limit Process to Find the Slope of the Graph