Determine the maximum value of y = 3x2 - x3
A
zero
B
2
C
4
D
6
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
y = 3x2 - x3
dy/dx = 6x - 3x2
as dy/dx = 0
6x - 3x2 = 0
3x (2 - x) = 0
this implies that 2 -x = 0 and 3x = 0
x = 2 (or) 0
But = dy/dx = 6x - 3x2
d2y/dx2 = 6 - 6x at x = 2
= 6 - 6(2)
= -6
y = 3x2 - x3
= 3(2)2 - 23
= 12 - 8
= 4
Source: Myschool Past Questions Archive (Record #7839)