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. $g ( x ) = \frac { 25 } { x }$
A) $m = - 1$
B) $m = 25$
C) $m = - 5$
D) $m = 5$
E) $m = - 25$

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.   $g ( x ) = \frac { 25 } { x }$  
A) $m = - 1$
B) $m = 25$
C) $m = - 5$
D) $m = 5$
E) $m = - 25$

Quizplus · Accepted Answer

The limit of the difference quotient as $h$ approaches 0 is the slope of the tangent line to the graph of $g$ at $x = 5$.$$\lim_{h\to 0} \frac{g(5+h)-g(5)}{h} = \lim_{h\to 0} \frac{\frac{25}{5+h}-\frac{25}{5}}{h} = \lim_{h\to 0} \frac{\frac{25(5)-25(5+h)}{5(5+h)}}{h}$$$$= \lim_{h\to 0} \frac{-25h}{5(5+h)} = \lim_{h\to 0} \frac{-5h}{5+h} = \lim_{h\to 0} \frac{-5}{5} = -1$$

Use the Limit Process to Find the Slope of the Graph