QPaperGen

We have:
\[
p(x) = 41 - 24x - 18x^2
\Rightarrow p'(x) = -24 - 36x
\Rightarrow p''(x) = -36 < 0
\]

Set derivative to zero:
\[
p'(x) = 0 \Rightarrow -24 - 36x = 0 \Rightarrow x = -\frac{2}{3}
\]

By second derivative test, local maximum occurs at \( x = -\frac{2}{3} \)

Now, compute:
\[
p\left( -\frac{2}{3} \right) = 41 - 24\left( -\frac{2}{3} \right) - 18\left( -\frac{2}{3} \right)^2
= 41 + 16 - 8 = 49
\]
\(\textbf{Maximum profit}\) = 49