logo

Ask Questions, Get Answers

X
 
Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives

Find the maximum profit that a company can make if the profit function is given by \[P(x)=41-24x-18x^2\]

1 Answer

Toolbox:
  • Necessary condition for maximum or minimum 'p' is $ \large\frac{dp}{dx}=0$
  • Condition for maximum is $ \large\frac{d^2p}{dx^2}$ is negative.
Step 1
$ \large\frac{dp}{dx}=-24-36x=0$
$ \Rightarrow x = - \large\frac{2}{3}$
Step 2
$ \large\frac{d^2p}{dx^2}=-36$ is negative
Step 3
maximum profit = $ p\bigg( \large\frac{-2}{3} \bigg) $$= 49$
answered Apr 11, 2013 by thanvigandhi_1
edited May 13, 2014 by balaji.thirumalai
 

Related questions

...