**Option : (B)**

f(x) = x^{3} – 6x^{2} + 9x, x ∈ [0,6]

**Differentiating f(x) with respect to x, we get **

f’(x)= 3x^{2} - 12x + 9 = 3(x - 3)(x - 1)

**For extreme points, **

f’(x) = 0

⇒ x = 1 or x = 3

**For least and greatest value of f(x) in [0,6], we will have to check at extreme points as well as interval extremes **

f(1) = 4

f(3) = 0

f(0) = 0

f(6) = 54

**Hence the least value of f(x) in [0,6] is 0 and it’s greatest value is 54.**