Question

how should you choose two nonnegative numbers whose sum is 1 in order to maximize the product of the square of one of them and the cube of the other?

Answer 1

we have 2 equations according information above :
x + y = 1 or y = 1 - x .... (1)
x^2 y^3 (assumed it has equal K)
so, K = x^2y^3 ... (2)

Answer 2

subtitute (1) to (2)
K = x^2y^3
K = x^2(1-x)^3

now, can u get the first derivative (K') of K ?

Answer 3

hint : use the produc rule, also the chain rule

Answer 4

if K = u v then K' = vu' + uv'

Answer 5

@syounge673

Answer 6

i don't understand