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2003
Mathematics
JAMB
Determine the maximum value of y = 3x
2
- x
3
A.
zero
B.
2
C.
4
D.
6
Correct Answer:
4
Explanation
y = 3x
2
- x
3
dy/dx = 6x - 3x
2
as dy/dx = 0 6x - 3x
2
= 0 3x (2 - x) = 0 this implies that 2 -x = 0 and 3x = 0 x = 2 (or) 0 But = dy/dx = 6x - 3x
2
d
2
y/dx
2
= 6 - 6x at x = 2 = 6 - 6(2) = -6 y = 3x
2
- x
3
= 3(2)
2
- 2
3
= 12 - 8 = 4
y = 3x
2
- x
3
dy/dx = 6x - 3x
2
as dy/dx = 0 6x - 3x
2
= 0 3x (2 - x) = 0 this implies that 2 -x = 0 and 3x = 0 x = 2 (or) 0 But = dy/dx = 6x - 3x
2
d
2
y/dx
2
= 6 - 6x at x = 2 = 6 - 6(2) = -6 y = 3x
2
- x
3
= 3(2)
2
- 2
3
= 12 - 8 = 4
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