Find the value of x for which the function 3x\(^3\) – 9x\(^2\) is minimum
- zero
-
2
- 3
- 5
The correct answer is: B
Explanation
y = 3x\(^3\) - 9x\(^2\)
dy/dx = 9x\(^2\) - 18x
As dy/dx = 0
9x\(^2\) - 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 = 2d\(^2\)y/dx\(^2\) = 18
∴ the value > 0 x is minimum