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  • Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 36 maths textbook solution.

Please solve RD Sharma class 12 Chapter Maxima and Minima exercise Multiple choice question, question 36 maths textbook solution.

Answers (1)

Answer: (c) One Maximum and One Minimum

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

Given: f(x)=2x^3-3x^2-12x+4

Solution:

Slope of the curve is given by,

f(x)=2x^3-3x^2-12x+4

f'(x)=6x^2-6x-12           

For maxima and minima f'(x)=0

\begin{aligned} &\Rightarrow 6 x^{2}-6 x-12=0 \\ &\Rightarrow x^{2}-x-2=0 \\ &\Rightarrow x=\frac{1 \pm \sqrt{1-4 \times 1 \times-2}}{2} \\ &x=\frac{1 \pm 3}{2} \\ &x=2,-1 \\ &f^{\prime \prime}(x)=12 x-6 \\ &f^{\prime \prime}(2)=12(2)-6=24-6=18>0 \end{aligned}

So, x = 2 is local minima.

f''(-1)=12(-1)-6=-12-6=-18<0

So, x = -1 is local maxima.

Therefore, One Maxima and One Minima is the answer.

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