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  • explain solution RD Sharma class 12 chapter Mean Value Theoram exercise 14.2 question 5 maths

explain solution RD Sharma class 12 chapter Mean Value Theoram exercise 14.2 question 5   maths

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Answer:  \left(\frac{9}{2}, \frac{1}{4}\right)

Hint: You must know the value of tangent parabola.

Given:y=(x-4)^{2} parallel to chord: (4,0)(5,1)

Solution:

y=(x-4)^{2}

Since tangent is parallel to chord joining (3, 0) and (4, 1), so, we get:

2(x-4)=\frac{1-0}{5-4}

\begin{aligned} &2 x-8=\frac{1}{1} \\ &2 x=9 \end{aligned}

x=\frac{9}{2}

\begin{aligned} &\text { When } &x=\frac{9}{2}, \text { then } y=\left(\frac{9}{2}-4\right)^{2} \end{aligned}

\begin{aligned} &=\left(\frac{9-8}{2}\right)^{2} \\ &=\left(\frac{1}{2}\right)^{2} \\ &=\frac{1}{4} \end{aligned}

Hence, the point is \left(\frac{9}{2}, \frac{1}{4}\right) .

 

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