Fun

find the difference quotient of f;

that is, find f(x+h)-f(x)/h, h=0,

for the following function  f(x)=2x+7

$\begin{array}{|rclrcl|} \hline &&& \frac {\Delta y}{\Delta x} &=& {\frac {f(x+h)-f(x)}{h}} \\ f(x) &=& 2x+7 \\ f(x+h) &=& 2(x+h)+7 \\ &&& \frac {\Delta y}{\Delta x} &=& {\frac {2(x+h)+7 -( 2x+7 ) }{h}} \\ &&& \frac {\Delta y}{\Delta x} &=& {\frac {\not{2x}+2h+\not{7} -\not{2x}-\not{7} }{h}} \\ &&& \frac {\Delta y}{\Delta x} &=& {\frac { 2h }{h}} \\ &&& \frac {\Delta y}{\Delta x} &=& {\frac { 2\not{h} }{\not{h}}} \\ &&& \frac {\Delta y}{\Delta x} &=& 2 \\ \hline \end{array}$