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

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- Sep 4th 2008, 07:52 PMNotEinsteinsimplify 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 PMChris L T521
- Sep 4th 2008, 08:19 PMNotEinstein
- Sep 4th 2008, 08:27 PMChris L T521
First expand $\displaystyle (x+h)^2$

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

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

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