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  • Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 5 maths textbook solution.

Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 5 maths textbook solution.

Answers (1)

Answer: Option (b) a minimum at x = 1  

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

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

Solution:

We have,

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

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

For maxima and minima f'(x)=0

\Rightarrow 3x^2+6x-9=0

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

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

\Rightarrow x=-3,1

Now,

f''(x)=6x+6

f''(1)=12>0

So, x =1 is a point of local minima.

Also, f''(-3)=-18 +6=-12<0

So, x = -3 is a point of local maxima.

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