Answer :

Let the two numbers are x and y such that x + y = 60

y = 60 –x


Let f(x) = xy3


f(x) = x(60-x)3


f’(x) = (60 –x)3 -3x(60 –x)2


= (60-x)2[60 – x – 3x]


= (60-x)2[60 – 4x]


And f’’(x) = -2(60 – x)(60 -4x) -4(60-x)2


= -2(60 – x)[60 -4x + 2(60-x)]


= -2(60 – x)(180 – 6x)


= -12(60 – x)(30 -x)


Now, f’(x) =0


x = 60 or x =15


When x = 60, f’’(x) = 0.


When x = 15, f’’(x) = -12(60-15)(30-15) = -12×45×15 < 0


Then, by second derivative test, x =15 is a point of local maxima of f.


Then, function xy3 is maximum when x =15 and y = 60 – 15 = 45.


Therefore, required numbers are 15 and 45.


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
caricature
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