#Mark the correct alternative in each of the following
The least and greatest values of f(x) = x3 – 6x2 + 9x in [0, 6], are
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.