Average Rate Of Change

Jul 2010
55
0
What is the average rate of change between x and x + h for the function \(\displaystyle f(x)=(2x+4)/x\) . Show your simplification.
 
Jan 2010
278
138
\(\displaystyle f(x)=\dfrac{2x+4}{x}\)

Find f(x + h):
\(\displaystyle f(x)=\dfrac{2(x+h)+4}{x+h} = \ldots\)

Plug f(x + h) and f(x) into
\(\displaystyle \dfrac{f(x + h) - f(x)}{h}\)
and simplify.
 
Last edited:
  • Like
Reactions: ilovemymath

Ackbeet

MHF Hall of Honor
Jun 2010
6,318
2,433
CT, USA
\(\displaystyle \dfrac{f(x + h) - f(h)}{h}\) is incorrect. It should be

\(\displaystyle \dfrac{f(x + h) - f(x)}{h}.\) That's the slope of the secant line, which also happens to be equal to the average rate of change.

[EDIT] Typo fixed.
 
Last edited:
  • Like
Reactions: ilovemymath
Jan 2010
278
138
Yes, of course. Fixed now.