Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

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

need solution for RD Sharma maths class 12 chapter Mean Value Theoram exercise 14.2 question 1 sub question (iii)

Answers (1)

Answer:   \frac{3}{2}

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

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

Solution:

f(x)=x(x-1)=x^{2}-x

f(x) is a polynomial function.

It is continuous in [1, 2] 

f^{\prime}(x)=2 x-1

(Which is defined in [1, 2])

\therefore f(x)  is differentiable in [1, 2]. Hence it satisfies the condition of Lagrange’s Mean Value Theorem.

Now, there exists at least one value,

\begin{aligned} &c \in[1,2] \\ &f^{\prime}(c)=\frac{f(2)-f(1)}{2-1} \\ &2 c-1=\frac{\left(2^{2}-2\right)-\left(1^{2}-1\right)}{1} \end{aligned}

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

 

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