JEE Exam > JEE Questions > The maximum value ofisa)(1/e)1/eb)(e)2...
Start Learning for Free
The maximum value of 
is
is- a)(1/e)1/e
- b)(e)2/e
- c)(e)-1/e
- d)(e)1/e
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrec...
Free Test
FREE
| Start Free Test |
Community Answer
The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrec...
For every real number (or) valued function f(x), the values of x which satisfies the equation f1(x)=0 are the point of it's local and global maxima or minima.
This occurs due to the fact that, at the point of maxima or minima, the curve of the function has a zero slope.
We have function f(x) = (1/x)x
We will be using the equation, y = (1/x)x
Taking in both sides we get
ln y = −xlnx
Differentiating both sides with respect to x.y.
dy/dx = −lnx−1
dy/dx =−y(lnx+1)
Equating dy/dx to 0, we get
−y(lnx+1)=0
Since y is an exponential function it can never be equal to zero, hence
lnx +1 = 0
lnx = −1
x = e(−1)
So, for the maximum value we put x = e^(−1)in f(x) to get the value of f(x) at the point.
f(e^−1) = e(1/e).
Hence the maximum value of the function is (e)1/e
This occurs due to the fact that, at the point of maxima or minima, the curve of the function has a zero slope.
We have function f(x) = (1/x)x
We will be using the equation, y = (1/x)x
Taking in both sides we get
ln y = −xlnx
Differentiating both sides with respect to x.y.
dy/dx = −lnx−1
dy/dx =−y(lnx+1)
Equating dy/dx to 0, we get
−y(lnx+1)=0
Since y is an exponential function it can never be equal to zero, hence
lnx +1 = 0
lnx = −1
x = e(−1)
So, for the maximum value we put x = e^(−1)in f(x) to get the value of f(x) at the point.
f(e^−1) = e(1/e).
Hence the maximum value of the function is (e)1/e
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer?
Question Description
The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer?.
The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The maximum value ofisa)(1/e)1/eb)(e)2/ec)(e)-1/ed)(e)1/eCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
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