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  • Explain solution RD Sharma class 12 chapter Maxima and Minima exercise Multiple choice question, question 27 maths

Explain solution RD Sharma class 12 chapter Maxima and Minima exercise Multiple choice question, question 27 maths

Answers (1)

Answer: option (b) -1

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

Given: f(x)=2x^3-3x^2-12x+5

Solution:

We have,

f(x)=2x^3-3x^2-12x+5                                                    

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-2)(x+1)=0 \\ &\Rightarrow x=2,-1 \end{aligned}

Now,

f''(x)=12x-6

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

So, x = -1 is the local maxima.

f''(2)=12(2)-6=24-6=18>0

So, x = 2 is the local minima.

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