Find the value of x for which the function 3x3 ... - JAMB Mathematics 2006 Question
Find the value of x for which the function 3x3 - 9x is minimum
A
zero
B
2
C
3
D
5
correct option: b
y = 3x3 - 9x2
dy/dx = 9x2 - 18x
As dy/dx = 0
9x2 - 18x = 0
9x(x-2) = 0
9x = 0 which implies x = 0
x-2 = 0 implies x = 2
d2y/dx2 = 18x - 18
when x = 0
d2y/dx2 < 0 ∴ x is is minimum
when x = 2d2y/dx2 = 18
∴ > 0 x is minimum
dy/dx = 9x2 - 18x
As dy/dx = 0
9x2 - 18x = 0
9x(x-2) = 0
9x = 0 which implies x = 0
x-2 = 0 implies x = 2
d2y/dx2 = 18x - 18
when x = 0
d2y/dx2 < 0 ∴ x is is minimum
when x = 2d2y/dx2 = 18
∴ > 0 x is minimum
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