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

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 $\left(\frac{9}{2}, \frac{1}{4}\right) .$