Mechanical Engineering Exam  >  Mechanical Engineering Questions  >  The function Y=| 2-3x | a)is continuous x R ... Start Learning for Free
The function Y=| 2-3x |  
  • a)
    is continuous ∀ x∈ R and differentiable ∀ x ∈ R
  • b)
    is continuous ∀ x∈ R and differentiable ∀ x ∈ R except at x = 3/2
  • c)
    is continuous ∀ x∈ R  and differentiable ∀ x ∈ R except at x = 2/3
  • d)
    is continuous ∀ x∈ R except at x = 3 and differentiable ∀ x ∈ R
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The function Y=| 2-3x | a)is continuous x R and differentiable x Rb...
Continuity of the function:
To determine the continuity of the function Y = |2-3x|, we need to check if the function is continuous at every point in its domain, which is all real numbers.

The function Y = |2-3x| can be written as two separate functions depending on the value of (2-3x).

When (2-3x) ≥ 0, the function becomes Y = 2-3x.
When (2-3x) < 0,="" the="" function="" becomes="" y="-(2-3x)" =="" />

Case 1: (2-3x) ≥ 0:
In this case, Y = 2-3x.
The function Y = 2-3x is a linear function and is continuous for all real numbers.

Case 2: (2-3x) < />
In this case, Y = -(2-3x) = 3x-2.
The function Y = 3x-2 is also a linear function and is continuous for all real numbers.

Combining the two cases:
Since both cases result in linear functions that are continuous for all real numbers, we can conclude that the function Y = |2-3x| is continuous for all real numbers.

Differentiability of the function:
To determine the differentiability of the function Y = |2-3x|, we need to check if the derivative exists at every point in its domain.

The derivative of the function Y = |2-3x| can be calculated by applying the chain rule.
When (2-3x) ≥ 0, the derivative is -3.
When (2-3x) < 0,="" the="" derivative="" is="" />

Case 1: (2-3x) ≥ 0:
In this case, the derivative is -3. The function Y = |2-3x| is differentiable for all x where (2-3x) ≥ 0.

Case 2: (2-3x) < />
In this case, the derivative is 3. The function Y = |2-3x| is differentiable for all x where (2-3x) < />

Combining the two cases:
The function Y = |2-3x| is differentiable for all real numbers except for the points where (2-3x) = 0, which is x = 2/3.

Conclusion:
Based on the analysis above, we can conclude that the function Y = |2-3x| is continuous for all real numbers and differentiable for all real numbers except at x = 2/3. Therefore, the correct answer is option 'C'.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. Can you explain this answer?
Question Description
The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. 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 The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The function Y=| 2-3x | a)is continuous x R and differentiable x Rb)is continuous x R and differentiable x R except at x = 3/2c)is continuous x R and differentiable x R except at x = 2/3d)is continuous x R except at x = 3 and differentiable x RCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev