Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

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

Please solve RD Sharma class 12 chapter Mean Value Theoram exercise 14.2 question 1 sub question (ix) maths textbook solution

Answers (1)

best_answer

Answer:  \pm \frac{1}{\sqrt{2}}

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

Given:f(x)=\sqrt{25-x^{2}} \text { on }[-3,4]

Solution:

f(x)=\sqrt{25-x^{2}}

f(x)  is a polynomial function.

It is continuous in [-3, 4] 

\begin{aligned} &f^{\prime}(x)=\frac{1}{2}\left(25-x^{2}\right)^{\frac{-1}{2}}(-2 x) \\ &f^{\prime}(x)=\frac{-x}{\sqrt{25-x^{2}}} \end{aligned}

(Which is defined in [-3, 4])

\therefore f(x) is differentiable in [-3, 4]. Hence it satisfies the condition of Lagrange’s Mean Value Theorem.

Now, there exists at least one value,

\begin{aligned} &c \in[-3,4] \\ &f^{\prime}(c)=\frac{f(4)-f(-3)}{4-(-3)} \end{aligned}

\begin{aligned} &\frac{-c}{\sqrt{25-c^{2}}}=\frac{\sqrt{25-(4)^{2}}-\sqrt{25-(-3)^{2}}}{4+3} \\ &\frac{-c}{\sqrt{25-c^{2}}}=\frac{\sqrt{25-16}-\sqrt{25-9}}{7} \end{aligned}

\begin{aligned} &\frac{-c}{\sqrt{25-c^{2}}}=\frac{\sqrt{9}-\sqrt{16}}{7} \\ &\frac{-c}{\sqrt{25-c^{2}}}=\frac{3-4}{7} \\ &\frac{-c}{\sqrt{25-c^{2}}}=\frac{-1}{7} \end{aligned}

\begin{aligned} &-7 c=-\sqrt{25-c^{2}} \\ &7 c=\sqrt{25-c^{2}} \end{aligned}

Squaring on both sides,

\begin{aligned} &49 c^{2}=25-c^{2} \\ &49 c^{2}+c^{2}-25=0 \\ &50 c^{2}-25=0 \end{aligned}

\begin{aligned} &2 c^{2}-1=0 \\ &2 c^{2}=1 \\ &c^{2}=\frac{1}{2} \\ &c^{2}=\pm \frac{1}{\sqrt{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

CBSE Board exams twice a year from 2025, no plan for semesters: MoE
anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question