Q. 163.8( 32 Votes )

# Find two positive

Answer :

Let one number be x. Then, the other number is (16 – x).

Let S(x) be the sum of these number. Then,

S(x) = x3 + (16-x)3

S’(x) = 3x2 -3(16-x)2

S’’(x) = 6x + 6(16-x)

Now, S’(x) =0

3x2 -3(16-x)2 = 0

x2 -(16-x)2 = 0

x2 – 256 - x2 + 32x = 0

x = 8

Now, S’’(8) = 6(8) + 6(16-8)

= 48 + 48 = 96 > 0

Then, by second derivative test, x = 8 is the point of local minima of S.

Therefore, the sum of the cubes of the numbers is the minimum when the numbers are 8 and 16-8 = 8.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

If the sum of theMathematics - Board Papers

A metal box with Mathematics - Board Papers

Show that aRD Sharma - Volume 1

Find the local maMathematics - Board Papers

Prove that the seMathematics - Board Papers

Prove that the raMathematics - Board Papers

Prove that the leMathematics - Board Papers