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  • Need solution for RD Sharma maths class 12 chapter Maxima and Minima exercise Multiple Choice question, question 17.

Need solution for RD Sharma maths class 12 chapter Maxima and Minima exercise Multiple Choice question, question 17.

Answers (1)

Answer: least=0,  greatest=54

Hint: For local maxima or minima, we must have f'(x)=0.

Given: f(x)=x^3-6x^2+9x

Solution:

We have,

f(x)=x^3-6x^2+9x

\Rightarrow f'(x)=3x^2-12x+9                                         

For maxima and minima f'(x)=0

\Rightarrow 3x^2-12x+9=0

\Rightarrow x^2-4x+3=0

\Rightarrow (x-1)(x-3)=0

\Rightarrow x=1,3

Now,

f(1)=1^3-6(1)^2+9(1)=1-6+9=4

f(3)=3^3-6(2)^2+9(6)=27-54+27=0

And at the extreme point of [0, 6]

f(0)=0^3-6(0)^2+9(0)=0

f(6)=6^3-6(6)^2+9(6)=216-216+54=54

The least and greatest values of f(x)=x^3-6x^2+9x  in (0 ,6) are 0 and 54.

Note: Option is not matching with the answer, given in the book.

Posted by

infoexpert24

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