Find the two numbers whose sum is 8, if the product of one number and the cube of the other is a maximum value?

Question

ganeshie8 · Answer

this is calculus.. .?

anonymous · Answer

yup 
yet is the answer is 2,6

hesan · Answer

HOW?

hesan · Answer

@matricked: u r right, can u please explain me..?

anonymous · Answer

if one number is x
then u have to maximise x^3(8-x)
on simply differentiating u get the values either 0 or 6
and then test for max condition using second order

hesan · Answer

What is meant by maximum value here?

anonymous · Answer

it means max value of x^3(8-x)

hesan · Answer

Okey, how will we maximise x^3(8-x)? By equating it to what?

anonymous · Answer

if u equate it to something then u willsolve for such particular values of x satisfying ur choice
u need to differentiate x^3(8-x)  and obtain 24x2-4x3and equate it to0 
to obtain the values of x(extremums) as x=0,6

hesan · Answer

i m not getting it...

anonymous · Answer

if u equate 24x2-4x3=0 thn the values of x is 0 or 6....

hesan · Answer

24x2-4x3=0 or 24x^2-4x^3=0   ?

anonymous · Answer

24x^2-4x^3=0 ?

hesan · Answer

where are the powers in 24x2-4x3=0

anonymous · Answer

generally its understood...

hesan · Answer

if we multiply 3x^2(8-x) then we'll get 24x^2-3x^3..