Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.

16. Find two positive numbers whose sum is 16 and the sum of whose cubes is
minimum.

Answers (1)

best_answer

let x an d y are positive two numbers 
It is given that 
x + y = 16 , y = 16 - x 
and  x^3 + y^3 is minimum
f(x) = x^3 + (16-x)^3
Now, 
f^{'}(x) = 3x^2 + 3(16-x)^2(-1)
f^{'}(x) = 0\\ 3x^2 - 3(16-x)^2 =0\\ 3x^2-3(256+x^2-32x) = 0\\ 3x^2 -3x^2+96x-768= 0\\ 96x = 768\\ x = 8\\
Hence, x = 8 is the only critical point 
Now,
f^{''}(x) = 6x - 6(16-x)(-1) = 6x + 96 - 6x = 96\\ f^{''}(x) = 96
f^{''}(8) = 96 > 0
Hence, x = 8 is the point of minima
 y = 16 - x
    = 16 - 8 = 8
Hence, values of x and y are 8  and 8 respectively 

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

Latest Question