JEE Exam > JEE Questions > Let f(x) be a function such that f'(a) &n...
Start Learning for Free
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)
- a)cannot have a maximum
- b)cannot have a minimum
- c)must have neither a maximum nor a minimum
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a...
Let f(x) = |x|.
f'(0) ≠ 0 but f(x) has a minimum at x = 0.
f'(0) ≠ 0 but f(x) has a minimum at x = 0.
Most Upvoted Answer
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a...
Explanation:
Nonzero Value at x = a
- Given that f(a) ≠ 0, meaning the function has a nonzero value at x = a.
Understanding Maximum and Minimum Points
- At a maximum point, the derivative of the function changes from positive to negative.
- At a minimum point, the derivative changes from negative to positive.
Analysis of Options
- Option A: Cannot have a maximum: Since f(a) ≠ 0, the function can have a maximum at x = a.
- Option B: Cannot have a minimum: Since f(a) ≠ 0, the function can have a minimum at x = a.
- Option C: Must have neither a maximum nor a minimum: This statement is not true as the function can have a maximum, minimum, or neither at x = a depending on the behavior of the function around that point.
- Option D: None of these: This is the correct answer as the function can have a maximum, minimum, or neither at x = a depending on the function's behavior.
Therefore, the correct answer is option D. None of these. The presence of a nonzero value at x = a does not restrict the function from having a maximum or minimum at that point.
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
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect 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 Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect 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 Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect answer is option 'D'. Can you explain this answer?.
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect 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 Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect 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 Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect 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 Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect 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!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup