Mechanical Engineering Exam > Mechanical Engineering Questions > Which of the following functions is not diffe...
Start Learning for Free
Which of the following functions is not differenti
able in the domain [-1,1]?
a)f(x) =
Maximum (x,-x) b)f(x) = x-1
c)f(x) = 2
d)f(x) =
x2Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which of the following functions is not differenti... moreable in the ...
Most Upvoted Answer
Which of the following functions is not differenti... moreable in the ...
Explanation:
- f(x) = Maximum (x,-x)
This function is not differentiable in the domain [-1,1] because it has a sharp corner or cusp at x = 0. The function is defined as the maximum of x and -x, which results in a V-shaped graph with a sharp point at x = 0. At this point, the function is not smooth and the derivative does not exist.
- Definition of Differentiability
A function is differentiable at a point if it has a well-defined derivative at that point. The derivative represents the rate of change of the function at that point. In the case of a sharp corner or cusp, the derivative does not exist because the function is not smooth at that point.
- Differentiability of Other Functions
b) f(x) = x-1
This function is differentiable everywhere, including the domain [-1,1], as it is a linear function with a constant slope.
c) f(x) = 2
This function is a constant function and is differentiable everywhere, including the domain [-1,1], as the rate of change is zero at every point.
d) f(x) = x^2
This function is differentiable everywhere, including the domain [-1,1], as it is a smooth curve without any sharp corners or cusps.
- Conclusion
In summary, the function f(x) = Maximum (x,-x) is not differentiable in the domain [-1,1] due to the presence of a sharp corner or cusp at x = 0. This function does not have a well-defined derivative at that point, unlike the other functions mentioned.
- f(x) = Maximum (x,-x)
This function is not differentiable in the domain [-1,1] because it has a sharp corner or cusp at x = 0. The function is defined as the maximum of x and -x, which results in a V-shaped graph with a sharp point at x = 0. At this point, the function is not smooth and the derivative does not exist.
- Definition of Differentiability
A function is differentiable at a point if it has a well-defined derivative at that point. The derivative represents the rate of change of the function at that point. In the case of a sharp corner or cusp, the derivative does not exist because the function is not smooth at that point.
- Differentiability of Other Functions
b) f(x) = x-1
This function is differentiable everywhere, including the domain [-1,1], as it is a linear function with a constant slope.
c) f(x) = 2
This function is a constant function and is differentiable everywhere, including the domain [-1,1], as the rate of change is zero at every point.
d) f(x) = x^2
This function is differentiable everywhere, including the domain [-1,1], as it is a smooth curve without any sharp corners or cusps.
- Conclusion
In summary, the function f(x) = Maximum (x,-x) is not differentiable in the domain [-1,1] due to the presence of a sharp corner or cusp at x = 0. This function does not have a well-defined derivative at that point, unlike the other functions mentioned.
Free Test
FREE
| Start Free Test |
Community Answer
Which of the following functions is not differenti... moreable in the ...
Correct answer should be 'd'. I think you all know why.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer?
Question Description
Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer?.
Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer?.
Solutions for Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which of the following functions is not differenti... moreable in the domain [-1,1]?a)f(x) =Maximum (x,-x)b)f(x) = x-1c)f(x) = 2d)f(x) =x2Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup