1. ## Maximum

The sum of two positive numbers is 5. What is the value of the larger number if the product of the smaller number and the cube of the larger is a maximum?

a. 5
b. 15/4
c. 5/4
d.1
e.0

2. So a + b = 5 and some f(x) = a(b)^3.

a = 5-b

$f(x) = (5-b)(b^3) = 5b^3 - b^4$

Max occurs at f'(x) = 0

$15b^2 - 4b^3 = 0$

$b^2(15-4b) = 0$

b = 0, 15/4

f''(15/4) < 0