Find the value of x for which the function 3×3 – 9x is minimum

Find the value of x for which the function 3x³ – 9x is minimum

Correct Answer: Option B

Explanation

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
when x = 2d²y/dx² = 18
∴ > 0 x is minimum