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Math Help - Simplify then find derivative

  1. #1
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    Simplify then find derivative

    Hi All,


    Can you help me with this please.


    For this function below simplify f(x + h) f(x) / h


    then take lim to find the derivative.
    h → 0

    f(x) = x+ 3x + 2 =
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  2. #2
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    To me, this is a calculus question, not a pre-calculus question.

    f(x) = x^2 + 3x + 2

    \begin{aligned}<br />
f(x+h) &= (x+h)^2 + 3(x+h) + 2 \\<br />
&= x^2 + 2hx + h^2 + 3x + 3h + 2 \\<br />
&= x^2 + (2h + 3)x + (h^2 + 3h + 2)<br />
\end{aligned}

    \begin{aligned}<br />
\frac{f(x+h) - f(h)}{h} &= \frac{[x^2 + (2h + 3)x + (h^2 + 3h + 2)] - [x^2 + 3x + 2]}{h} \\<br />
&= \frac{2hx + h^2 + 3h}{h} \\<br />
&= \frac{h(2x + h + 3)}{h} \\<br />
&= 2x + h + 3<br />
\end{aligned}

    \lim_{h \to 0} (2x + h + 3) = 2x + 3


    01
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  3. #3
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    Thanks,

    Posted without analysis of the appropriate section and could not figure out how to shift it into the correct section.

    You explanation is very clear. Excellent job
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