Mathematics

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
  • A.
    zero
  • B.
    2
  • C.
    3
  • D.
    5
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