Quant Exam > Quant Questions > Which of the following functions will have a ...
Start Learning for Free
Which of the following functions will have a minimum value at x = –3?
- a)f(x) = 2x3 – 4x + 3
- b)f(x) = 4x4 – 3x + 5
- c)f(x) = x6 – 2x – 6
- 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
Which of the following functions will have a minimum value at x = R...
If you differentiate each function with respect to x, and equate it to 0 you would see that for none
of the three options will get you a value of x = –3 as its solution. Thus, option (d) viz. None of
these is correct.
of the three options will get you a value of x = –3 as its solution. Thus, option (d) viz. None of
these is correct.
Most Upvoted Answer
Which of the following functions will have a minimum value at x = R...
Explanation:
To determine which function will have a minimum value at x = 3, we need to analyze the behavior of each function in the vicinity of x = 3.
Function a: f(x) = 2x^3 - 4x + 3
- To find the minimum, we need to take the derivative of the function and set it equal to zero.
- Taking the derivative of f(x) with respect to x, we get: f'(x) = 6x^2 - 4
- Setting f'(x) = 0 and solving for x, we get: 6x^2 - 4 = 0
- Solving this quadratic equation, we find: x = ±√(4/6) = ±√(2/3)
- Since the roots of the derivative are not equal to 3, the function does not have a minimum at x = 3.
Function b: f(x) = 4x^4 - 3x + 5
- Taking the derivative of f(x) with respect to x, we get: f'(x) = 16x^3 - 3
- Setting f'(x) = 0 and solving for x, we get: 16x^3 - 3 = 0
- We can use numerical methods or approximations to find the root, but it is evident that the root is not 3.
- Therefore, the function does not have a minimum at x = 3.
Function c: f(x) = x^6 - 2x + 6
- Taking the derivative of f(x) with respect to x, we get: f'(x) = 6x^5 - 2
- Setting f'(x) = 0 and solving for x, we get: 6x^5 - 2 = 0
- We can use numerical methods or approximations to find the root, but it is evident that the root is not 3.
- Therefore, the function does not have a minimum at x = 3.
Conclusion:
None of the given functions have a minimum at x = 3.
To determine which function will have a minimum value at x = 3, we need to analyze the behavior of each function in the vicinity of x = 3.
Function a: f(x) = 2x^3 - 4x + 3
- To find the minimum, we need to take the derivative of the function and set it equal to zero.
- Taking the derivative of f(x) with respect to x, we get: f'(x) = 6x^2 - 4
- Setting f'(x) = 0 and solving for x, we get: 6x^2 - 4 = 0
- Solving this quadratic equation, we find: x = ±√(4/6) = ±√(2/3)
- Since the roots of the derivative are not equal to 3, the function does not have a minimum at x = 3.
Function b: f(x) = 4x^4 - 3x + 5
- Taking the derivative of f(x) with respect to x, we get: f'(x) = 16x^3 - 3
- Setting f'(x) = 0 and solving for x, we get: 16x^3 - 3 = 0
- We can use numerical methods or approximations to find the root, but it is evident that the root is not 3.
- Therefore, the function does not have a minimum at x = 3.
Function c: f(x) = x^6 - 2x + 6
- Taking the derivative of f(x) with respect to x, we get: f'(x) = 6x^5 - 2
- Setting f'(x) = 0 and solving for x, we get: 6x^5 - 2 = 0
- We can use numerical methods or approximations to find the root, but it is evident that the root is not 3.
- Therefore, the function does not have a minimum at x = 3.
Conclusion:
None of the given functions have a minimum at x = 3.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which of the following functions will have a minimum value at x = –3?a)f(x) = 2x3 – 4x + 3b)f(x) = 4x4 – 3x + 5c)f(x) = x6 – 2x – 6d)None of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup