Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 - 72 x -18 x^ 2

6. Find the maximum profit that a company can make, if the profit function is
given by  p(x) = 41 - 72x - 18x ^2

Answers (1)

best_answer

Profit of the company is given by the function 
p(x) = 41 - 72x - 18x ^2
p^{'}(x)= -72-36x\\ p^{'}(x) = 0\\ -72-36x= 0\\ x = -2
x = -2 is the only critical point of the function p(x) = 41 - 72x - 18x ^2
Now, by second derivative test
p^{''}(x)= -36< 0
At x = -2 p^{''}(x)< 0
Hence, maxima of function p(x) = 41 - 72x - 18x ^2 occurs at x = -2 and maximum value is
p(-2) = 41 - 72(-2) - 18(-2) ^2=41+144-72 = 113
Hence, the maximum profit the company can make is 113 units

Posted by

Gautam harsolia

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years
anam-khan

CBSE Class 12 accountancy board exam analysis 2024 out; paper rated easy, balanced

Latest Question