Q. 17

#Mark the correct alternative in each of the following

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 :

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





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

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