# Math Help - Help again, largest revenue and weekly profit

1. ## Help again, largest revenue and weekly profit

question again...

i need some guidance to see if im doing this right

-p^3 + 33p + 9
First i did (pq) then i took the derivative to find revenue which i got
-3p^2 +33p + 9p = 0 i need to find largest revenue with this equation

well i keep getting to -p^2 = -11p -3

is this right? or where do i go from here?

Also i had to do a cost equation and had to find what -3p^2 + 18p -265 = 0 i need to find largest weekly profit with this equation

I go to p^2= -88.3 + 6p

Same question here, did i get the right numbers or of i did what do i do to solve?

thank you : )

2. For the first problem, if we call the revenue $R$, we have

$R=pq=p(-p^3+33p+9)=-p^4+33p^2+9p.$

Differentiating, we obtain

\begin{aligned}
\frac{dR}{dp}&=\frac{d}{dp}(-p^4)+\frac{d}{dp}(33p^2)+\frac{d}{dp}(9p)\\
&=-4p^3+33\cdot2p+9\cdot 1\\
&=-4p^3+66p+9.
\end{aligned}

For the second problem, we may use the Quadratic Formula:

$ax^2+bx+c=0\quad\Rightarrow\quad x=-\frac{b}{2a}\pm\frac{1}{2a}\sqrt{b^2-4ac}.$