Option : (B)
f(x) = x3 – 6x2 + 9x, x ∈ [0,6]
Differentiating f(x) with respect to x, we get
f’(x)= 3x2 - 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.