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  • Please solve RD Sharma class 12 Chapter maxima and minima exercise 17.5 question 33 maths textbook solution.

Please solve RD Sharma class 12 Chapter maxima and minima exercise 17.5 question 33 maths textbook solution.

Answers (1)

(-2, -8)

Hint: For maximum or minimum value of S, we must have \frac{dS}{dt}=0

Given: Let coordinate of the point on the parabola be (x,y). Then,

y= x^2+7x +2                    ......(1)

Solution:  Let the distance of the point (x,(x^2+7x+2)) from the line y=3x-3 be S.

\begin{aligned} &\mathrm{S}=\left|\frac{-3 x+\left(x^{2}+7 x+2\right)+3}{\sqrt{10}}\right| \\ &\frac{d S}{d t}=\frac{-3+2 x+7}{\sqrt{10}} \\ &\frac{d S}{d t}=0 \\ &\frac{-3+2 x+7}{\sqrt{10}}=0 \\ &2 x=-4, x=-2 \\ &\frac{d^{2} S}{d t^{2}}=\frac{2}{\sqrt{10}}>0 \end{aligned}

The required nearest point is (x,(x^2+7x+2)) 

=(-2,4-14+2)

=(-2,-8)

 

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