Maxima and Minima word problems..?

Question

please help me answer these questions step-by-step..
1) Find two numbers whose sum is 9. If the product of one by the square of the other is a maximum.

2)The sum of the bases and the altitude of a trapezoid is 36 inches longer than the other. Find all three dimensions if the area is a maximum.

3)Find the shortest distance from the curve (y²=x³) to the point (8,0).

Help me please... T_T

Answer 1

x = one number
9-x = other number
f(x) = (9-x)(x^2) = 9x^2-x^3
f '(x) = 18x-3x^2 =0
3x(x-6) = 0
x = 6
= one number
9-x = 3 = other number

2) Unclear what "the other" is. Base1+base2 + altitude = 36 + what?

3) y^2=x^3
y = +/- x^3/2
dy/dx = 3/2x^1/2 = 0 --> x = 0
Henec shrtest distance is 8-0 = 8 units