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. $h ( x ) = \sqrt { x },(4,2)$

A) $m = \frac { 1 } { 4 }$
B) $m = - 2$
C) $m = 4$
D) $m = - \frac { 1 } { 4 }$
E) $m = 2$

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.   $h ( x ) = \sqrt { x },(4,2)$  
 
A) $m = \frac { 1 } { 4 }$
B) $m = - 2$
C) $m = 4$
D) $m = - \frac { 1 } { 4 }$
E) $m = 2$

Quizplus · Accepted Answer

The slope of the graph of the function $h(x) = \sqrt{x}$ at a point can be found using the derivative of the function. The derivative of $h(x) = \sqrt{x}$ is $h'(x) = \frac{1}{2\sqrt{x}}$. Plugging in the x-value of the specified point (4,2), we get $h'(4) = \frac{1}{2\sqrt{4}} = \frac{1}{4}$, which means the slope of the graph at the point (4,2) is $\frac{1}{4}$.

Use the Limit Process to Find the Slope of the Graph