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 =
To me, this is a calculus question, not a pre-calculus question.
$\displaystyle f(x) = x^2 + 3x + 2$
$\displaystyle \begin{aligned}
f(x+h) &= (x+h)^2 + 3(x+h) + 2 \\
&= x^2 + 2hx + h^2 + 3x + 3h + 2 \\
&= x^2 + (2h + 3)x + (h^2 + 3h + 2)
\end{aligned}$
$\displaystyle \begin{aligned}
\frac{f(x+h) - f(h)}{h} &= \frac{[x^2 + (2h + 3)x + (h^2 + 3h + 2)] - [x^2 + 3x + 2]}{h} \\
&= \frac{2hx + h^2 + 3h}{h} \\
&= \frac{h(2x + h + 3)}{h} \\
&= 2x + h + 3
\end{aligned}$
$\displaystyle \lim_{h \to 0} (2x + h + 3) = 2x + 3$
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