The sum of two numbers is 28. Find an absolute minimum of the sum of their cubes. ?

The sum of two numbers is 28.


Find the numbers given that the sum of their cubes is an absolute minimum.The sum of two numbers is 28. Find an absolute minimum of the sum of their cubes. ?
A + B = 28





A鲁 + B鲁 = min


A鲁 + ( 28 - A )鲁 = min





To find the value of A that yields a minimum, solve





d/dA [ A鲁 + ( 28 - A )鲁 ] = 0





Enjoy!The sum of two numbers is 28. Find an absolute minimum of the sum of their cubes. ?
x + y = 28





min(x鲁 + y鲁)


= min(x鲁 + (28 - x)鲁)





To find min solve:





d/dx(x鲁 + (28 - x)鲁) = 0


3x虏 - 3(28 - x)虏 = 0


3x虏 - 3(28虏 - 56x + x虏) = 0


3x虏 - 2352 + 168x - 3x虏 = 0


- 2352 + 168x = 0


168x = 2352


x = 2352/168


x = 14
x + y = 28


1 + dy/dx = 0





f(x,y) = x鲁 + y鲁


0 = 3x虏 + 3y虏 dy/dx


0 = 3x虏 + 3(28-x)虏(-1)


0 = x虏 - 784 + 56x - x虏


56x = 784


x = 14


y = 14





Answer: 14 and 14
14 and 14 its equal to 392