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

1.	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» 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.

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»

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.