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Math Help - simplify the difference quotient

  1. #1
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    simplify the difference quotient

    "simplify the difference quotient f(x+h)-f(x) over h whenever f(x)=2x^2+4x+2"
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by NotEinstein View Post
    "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
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  3. #3
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    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 View Post
    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
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by NotEinstein View Post
    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 View Post
    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
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