# simplify the difference quotient

• Sep 4th 2008, 07:52 PM
NotEinstein
simplify the difference quotient
"simplify the difference quotient f(x+h)-f(x) over h whenever f(x)=2x^2+4x+2"
• Sep 4th 2008, 07:55 PM
Chris L T521
Quote:

Originally Posted by NotEinstein
"simplify the difference quotient f(x+h)-f(x) over h whenever f(x)=2x^2+4x+2"

Where are you stuck?

$\frac{f(x+h)-f(x)}{h}\implies\frac{2(x+h)^2+4(x+h)+2-(2x^2+4x+2)}{h}$

Take it from here. Its just expanding and simplifying from here on out.

--Chris
• Sep 4th 2008, 08:19 PM
NotEinstein
I know this should be in algebra, but im confused where to start. I honestly havent done any of this in years.

Quote:

Originally Posted by Chris L T521
Where are you stuck?

$\frac{f(x+h)-f(x)}{h}\implies\frac{2(x+h)^2+4(x+h)+2-(2x^2+4x+2)}{h}$

Take it from here. Its just expanding and simplifying from here on out.

--Chris

• Sep 4th 2008, 08:27 PM
Chris L T521
Quote:

Originally Posted by NotEinstein
I know this should be in algebra, but im confused where to start. I honestly havent done any of this in years.

Quote:

Originally Posted by Chris L T521
Where are you stuck?

$\frac{f(x+h)-f(x)}{h}\implies\frac{2(x+h)^2+4(x+h)+2-(2x^2+4x+2)}{h}$

Take it from here. Its just expanding and simplifying from here on out.

--Chris

First expand $(x+h)^2$

$(x+h)^2=x^2+2hx+h^2$

Thus, the difference quotient becomes $\frac{2(x^2+2hx+h^2)+4(x+h)+2-2x^2-4x-2}{h}$ $=\frac{2x^2+4hx+2h^2+4x+4h+2-2x^2-4x-2}{h}$

Try to take it from here. See if you can finish simplifying this expression.

The remaining terms in the numerator should have at least one h.

--Chris