Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • explain solution RD Sharma class 12 chapter Mean Value Theoram exercise 14.2 question 1 sub question (viii) maths

explain solution RD Sharma class 12 chapter Mean Value Theoram exercise 14.2 question 1 sub question (viii) maths

Answers (1)

Answer:   4 \pm \frac{2}{\sqrt{3}}

Hint: You must know the formula of Lagrange’s Mean Value Theorem.

Given: f(x)=(x-1)(x-2)(x-3) \text { on }[0,4]

Solution:

\begin{aligned} &f(x)=(x-1)(x-2)(x-3) \\ &f(x)=x^{3}-6 x^{2}+11 x-6 \end{aligned}

f(x)  is a polynomial function.

It is continuous in [0, 4] 

f^{\prime}(x)=3 x^{2}-12 x+11

(Which is defined in [0, 4])

\therefore f(x) is differentiable in [0, 4]. Hence it satisfies the condition of Lagrange’s Mean Value Theorem.

Now, there exists at least one value,

\begin{aligned} &c \in[0,4] \\ &f^{\prime}(c)=\frac{f(4)-f(0)}{4-0} \end{aligned}

\begin{aligned} &3 c^{2}-12 c+11=\frac{(4-1)(4-2)(4-3)-(0-1)(0-2)(0-3)}{4} \\ &3 c^{2}-12 c+11=\frac{(3)(2)(1)-(-1)(-2)(-3)}{4} \end{aligned}

\begin{aligned} &3 c^{2}-12 c+11=\frac{6+6}{4} \\ &3 c^{2}-12 c+11=\frac{12}{4} \end{aligned}

\begin{aligned} &3 c^{2}-12 c+11=3 \\ &3 c^{2}-12 c+11-3=0 \\ &3 c^{2}-12 c+8=0 \end{aligned}

Quadratic Equation,

\begin{aligned} &c=\frac{12 \pm \sqrt{144-96}}{6} \\ &c=\frac{12 \pm \sqrt{48}}{6} \end{aligned}

\begin{aligned} &c=\frac{12 \pm 4 \sqrt{3}}{6} \\ &c=4 \pm \frac{2 \sqrt{3}}{3} \\ &c=4 \pm \frac{2}{\sqrt{3}} \end{aligned}

Both values lie between [0, 4]

 

 

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question