# Worded equation

#### scubasteve94

Find two positive numbers whose sum is 4 and such that the sum of te cube of the first an the square of the second is as small as possible.

Thanks any help would be appreciated!

Find two positive numbers whose sum is 4 and such that the sum of te cube of the first an the square of the second is as small as possible.

Thanks any help would be appreciated!
hi

let x and y be the two positive numbers ,

$$\displaystyle x+y = 4$$ -- 1

let $$\displaystyle f(x)=x^3+y^2$$

$$\displaystyle =x^3+(4-x)^2$$

$$\displaystyle =x^3+x^2-8x+16$$

$$\displaystyle f'(x)=3x^2+2x-8=(3x-4)(x+2)$$

When f'(x)=0 , x=4/3 or x=-2

x=4/3 is a local minimum and can be verified by taking the second derivative .

Thank you!!