# Math Help - Simplify then find derivative

1. ## 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) = x²+ 3x + 2 =

2. To me, this is a calculus question, not a pre-calculus question.

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

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

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

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

01

3. 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