Quant Exam > Quant Questions > The function f(x) = | x - 2| + | 2.5 - x| + |...
Start Learning for Free
The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum at
- a)x=2.3
- b)x=2.5
- c)x=2.4
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a re...
The best way of doing this question is to substitute the value of x in the option to the given expression in f(x).
We get the minimum value of 1.6 for f(x) when x=2.5.
Now, there is a question whether the minimum value of the expression can be lesser than this.
In order to resolve the ambiguity,plot f(x) vs x in the graph for x=1,2,3,4 and so on.
We find that the minimum value is acheived at x=2.5.
Hence option(2) is the answer.
Most Upvoted Answer
The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a re...
Solution:
To find the minimum value of the given function, we need to find the critical points of the function.
Critical points are the points where the derivative of the function is zero or the derivative does not exist.
Let's find the derivative of the given function.
f(x) = |x - 2| |2.5 - x| |3.6 - x|
f'(x) = [(x - 2) / |x - 2|] |2.5 - x| |3.6 - x| + |x - 2| [(2.5 - x) / |2.5 - x|] |3.6 - x| + |x - 2| |2.5 - x| [(x - 3.6) / |3.6 - x|]
Now, to find the critical points, we need to set f'(x) = 0 and solve for x.
[(x - 2) / |x - 2|] |2.5 - x| |3.6 - x| + |x - 2| [(2.5 - x) / |2.5 - x|] |3.6 - x| + |x - 2| |2.5 - x| [(x - 3.6) / |3.6 - x|] = 0
We can simplify this equation by dividing both sides by the common factor |x - 2| |2.5 - x| |3.6 - x|.
[(x - 2) / |x - 2|] + [(2.5 - x) / |2.5 - x|] + [(x - 3.6) / |3.6 - x|] = 0
Now, we can solve this equation by considering the three cases:
Case 1: x < />
In this case, we have:
[(x - 2) / (2 - x)] + [(2.5 - x) / (2.5 - x)] + [(x - 3.6) / (x - 3.6)] = 0
Simplifying this equation, we get:
x = 2.4
Case 2: 2.5 < x="" />< />
In this case, we have:
[(x - 2) / (x - 2)] + [(2.5 - x) / (2.5 - x)] + [(x - 3.6) / (x - 3.6)] = 0
This equation is not defined at x = 2.5 and x = 3.6. However, we can see that the function is continuous in this interval, and it attains its minimum value at x = 2.5. Therefore, x = 2.5 is a critical point.
Case 3: x > 3.6
In this case, we have:
[(x - 2) / (x - 2)] + [(2.5 - x) / (2.5 - x)] + [(x - 3.6) / (3.6 - x)] = 0
Simplifying this equation, we get:
x = 3
Therefore, the critical points of the function are x
To find the minimum value of the given function, we need to find the critical points of the function.
Critical points are the points where the derivative of the function is zero or the derivative does not exist.
Let's find the derivative of the given function.
f(x) = |x - 2| |2.5 - x| |3.6 - x|
f'(x) = [(x - 2) / |x - 2|] |2.5 - x| |3.6 - x| + |x - 2| [(2.5 - x) / |2.5 - x|] |3.6 - x| + |x - 2| |2.5 - x| [(x - 3.6) / |3.6 - x|]
Now, to find the critical points, we need to set f'(x) = 0 and solve for x.
[(x - 2) / |x - 2|] |2.5 - x| |3.6 - x| + |x - 2| [(2.5 - x) / |2.5 - x|] |3.6 - x| + |x - 2| |2.5 - x| [(x - 3.6) / |3.6 - x|] = 0
We can simplify this equation by dividing both sides by the common factor |x - 2| |2.5 - x| |3.6 - x|.
[(x - 2) / |x - 2|] + [(2.5 - x) / |2.5 - x|] + [(x - 3.6) / |3.6 - x|] = 0
Now, we can solve this equation by considering the three cases:
Case 1: x < />
In this case, we have:
[(x - 2) / (2 - x)] + [(2.5 - x) / (2.5 - x)] + [(x - 3.6) / (x - 3.6)] = 0
Simplifying this equation, we get:
x = 2.4
Case 2: 2.5 < x="" />< />
In this case, we have:
[(x - 2) / (x - 2)] + [(2.5 - x) / (2.5 - x)] + [(x - 3.6) / (x - 3.6)] = 0
This equation is not defined at x = 2.5 and x = 3.6. However, we can see that the function is continuous in this interval, and it attains its minimum value at x = 2.5. Therefore, x = 2.5 is a critical point.
Case 3: x > 3.6
In this case, we have:
[(x - 2) / (x - 2)] + [(2.5 - x) / (2.5 - x)] + [(x - 3.6) / (3.6 - x)] = 0
Simplifying this equation, we get:
x = 3
Therefore, the critical points of the function are x
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
Question Description
The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. 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 The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. 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 The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. 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 The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The function f(x) = | x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number, attains a minimum ata)x=2.3b)x=2.5c)x=2.4d)None of the aboveCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup