Determine the maximum value of y = 3x2 – x3
-
A.
zero -
B.
2 -
C.
4 -
D.
6
Correct Answer: Option C
Explanation
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