Question

The least and greatest values of f(x) = x³ – 6x² + 9x in [0, 6], are :

A. 3, 4 

B. 0, 6 

C. 0, 3 

D. 3, 6

Answer 1

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.