Class 11 Exam > Class 11 Questions > The maximum and minimum value of y=x+1/x in i...
Start Learning for Free
The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)?
Most Upvoted Answer
The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2....
Explanation:
Given, y = x 1/x in interval (1/3,4/3)
To find the maximum and minimum value of y, we differentiate y with respect to x and equate it to zero.
dy/dx = (1/x) - (1/x^2) = 0
x = 1
To confirm whether x = 1 is a point of maximum or minimum, we differentiate y^2 with respect to x and check its sign.
d(y^2)/dx = (2/x) - (2/x^3)
d(y^2)/dx at x = 1 is 0. Hence, we check the sign of d(y^2)/dx at x = 1 -
d(y^2)/dx at x = 0.9 is positive, and d(y^2)/dx at x = 1.1 is negative. Hence, x = 1 is a point of maximum.
Now, we substitute x = 1/3, 4/3 in y = x 1/x to find the minimum and maximum values of y.
y(1/3) = (1/3)^(3) = 1/27
y(4/3) = (4/3)^(3/4) = 2
Therefore, the maximum value of y is 2 and the minimum value of y is 1/27.
Answer:
The correct answer is option 2) 10/3, 2.
Given, y = x 1/x in interval (1/3,4/3)
To find the maximum and minimum value of y, we differentiate y with respect to x and equate it to zero.
dy/dx = (1/x) - (1/x^2) = 0
x = 1
To confirm whether x = 1 is a point of maximum or minimum, we differentiate y^2 with respect to x and check its sign.
d(y^2)/dx = (2/x) - (2/x^3)
d(y^2)/dx at x = 1 is 0. Hence, we check the sign of d(y^2)/dx at x = 1 -
d(y^2)/dx at x = 0.9 is positive, and d(y^2)/dx at x = 1.1 is negative. Hence, x = 1 is a point of maximum.
Now, we substitute x = 1/3, 4/3 in y = x 1/x to find the minimum and maximum values of y.
y(1/3) = (1/3)^(3) = 1/27
y(4/3) = (4/3)^(3/4) = 2
Therefore, the maximum value of y is 2 and the minimum value of y is 1/27.
Answer:
The correct answer is option 2) 10/3, 2.
Community Answer
The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2....
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)?
Question Description
The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)?.
The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)?.
Solutions for The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)? defined & explained in the simplest way possible. Besides giving the explanation of
The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)?, a detailed solution for The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)? has been provided alongside types of The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)? theory, EduRev gives you an
ample number of questions to practice The maximum and minimum value of y=x+1/x in interval (1/3,4/3) 1)2,-2. 2)10/3,2. 3) none of these. and the correct answer is 2)? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup