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 maxima and minima exercise 17.5 question 3 maths textbook solution.

Please solve RD Sharma class 12 Chapter maxima and minima exercise 17.5 question 3 maths textbook solution.

Answers (1)

\left (\frac{1}{2}-\frac{1}{\sqrt{3}} \right )\text{ and} \; \frac{1}{\sqrt{3}}

Hint: For maximum or minimum value of z must have \frac{dz}{dx}=0

Given: x,y >-2 and x+y =\frac{1}{2}

Solution: Let the numbers be x and y then

x,y >-2 and x+y =\frac{1}{2}                             .....(1)

\begin{aligned} &\text { Now, }\\ &z=x+y^{3}\\ &z=x+\left(\frac{1}{2}-x\right)^{3} \quad[\text { from }(1)]\\ &\frac{d z}{d x}=1+3\left(\frac{1}{2}-x\right)^{2} \end{aligned}

For maximum or minimum value of z

\frac{dz}{dx}=0

\begin{aligned} &1+3\left(\frac{1}{2}-x\right)^{2}=0 \\ &\left(\frac{1}{2}-x\right)^{2}=\frac{1}{3} \\ &\left(\frac{1}{2}-x\right)=\pm \frac{1}{\sqrt{3}} \\ &x=\frac{1}{2} \pm \frac{1}{\sqrt{3}} \end{aligned}

\begin{aligned} &\frac{d^{2} z}{d x^{2}}=3-6\left(\frac{1}{2}+\frac{1}{\sqrt{3}}\right) \\ &=\frac{-6}{\sqrt{3}}<0 \end{aligned}

\therefore z is minimum when x=\frac{1}{2}+\frac{1}{\sqrt{3}}

At x=\frac{1}{2}-\frac{1}{\sqrt{3}}

\begin{aligned} &\frac{d^{2} z}{d x^{2}}=3-6\left(\frac{1}{2}-\frac{1}{\sqrt{3}}\right) \\ &=\frac{-6}{\sqrt{3}}>0 \end{aligned}

\therefore z is minimum when x=\frac{1}{2}-\frac{1}{\sqrt{3}}

x+y = \frac{1}{2}

Substituting the value in (1)

\begin{aligned} &y=\frac{-1}{2}+\frac{1}{\sqrt{3}}+\frac{1}{2} \\ &y=\frac{1}{\sqrt{3}} \end{aligned}

So the two required numbers are \left (\frac{1}{2}-\frac{1}{\sqrt{3}} \right )\text{ and} \; \frac{1}{\sqrt{3}}

 

 

Posted by

infoexpert24

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