The profit function of a company is given by $P(x)=40-36 x-18 x^2$. The maximum profit that the company can make is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 58
$P(x)=40+36x-18x^2$
$\frac{dP}{dx}=36-36x$
$36-36x=0 \Rightarrow x=1$
$\frac{d^2P}{dx^2}=-36<0 \Rightarrow \text{maximum}$
$P(1)=40+36-18=58$
The maximum profit is $58$.