I ilovemymath Jul 2010 55 0 Aug 3, 2010 #1 What is the average rate of change between x and x + h for the function \(\displaystyle f(x)=(2x+4)/x\) . Show your simplification.

What is the average rate of change between x and x + h for the function \(\displaystyle f(x)=(2x+4)/x\) . Show your simplification.

eumyang Jan 2010 278 138 Aug 3, 2010 #2 \(\displaystyle f(x)=\dfrac{2x+4}{x}\) 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: Aug 3, 2010 Reactions: ilovemymath

\(\displaystyle f(x)=\dfrac{2x+4}{x}\) 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.

A Ackbeet MHF Hall of Honor Jun 2010 6,318 2,433 CT, USA Aug 3, 2010 #3 \(\displaystyle \dfrac{f(x + h) - f(h)}{h}\) 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: Aug 3, 2010 Reactions: ilovemymath

\(\displaystyle \dfrac{f(x + h) - f(h)}{h}\) 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.