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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : A continuous function is always differentiable.
Reason : A differentiable function is always continuous.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'D'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) ...
The function f(x) is differentiable at x = a, if it is continuous at x = a and LHD = RHD at x = a.
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A differentiable function is always continuous. Hence R is true.
A continuous function need not be always differentiable.
For example, |x| is continuous at x = 0, but not differentiable at x = 0.
Hence A is false.
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
Assertion: A continuous function is always differentiable.
Reason: A differentiable function is always continuous.
Explanation:
Continuous Function: A function is said to be continuous if it is defined and has no abrupt jumps or breaks in its graph. In other words, a function is continuous if its graph can be drawn without lifting the pen from the paper.
Differentiable Function: A function is said to be differentiable if it has a derivative at every point in its domain. The derivative of a function represents the rate at which the function is changing at a particular point.
Explanation of Assertion: The assertion statement that a continuous function is always differentiable is FALSE. There are many examples of continuous functions that are not differentiable. One such example is the absolute value function, f(x) = |x|. This function is continuous for all values of x, but it is not differentiable at x = 0 because the slope of the function changes abruptly at that point.
Explanation of Reason: The reason statement that a differentiable function is always continuous is TRUE. If a function is differentiable at a point, then it must be continuous at that point. This is because the derivative of a function measures the rate of change of the function, and if the derivative exists at a point, it means that the function is changing smoothly at that point without any abrupt jumps or breaks.
Conclusion: The correct answer is option D, A is false and R is true. A continuous function is not always differentiable, but a differentiable function is always continuous.
Reason: A differentiable function is always continuous.
Explanation:
Continuous Function: A function is said to be continuous if it is defined and has no abrupt jumps or breaks in its graph. In other words, a function is continuous if its graph can be drawn without lifting the pen from the paper.
Differentiable Function: A function is said to be differentiable if it has a derivative at every point in its domain. The derivative of a function represents the rate at which the function is changing at a particular point.
Explanation of Assertion: The assertion statement that a continuous function is always differentiable is FALSE. There are many examples of continuous functions that are not differentiable. One such example is the absolute value function, f(x) = |x|. This function is continuous for all values of x, but it is not differentiable at x = 0 because the slope of the function changes abruptly at that point.
Explanation of Reason: The reason statement that a differentiable function is always continuous is TRUE. If a function is differentiable at a point, then it must be continuous at that point. This is because the derivative of a function measures the rate of change of the function, and if the derivative exists at a point, it means that the function is changing smoothly at that point without any abrupt jumps or breaks.
Conclusion: The correct answer is option D, A is false and R is true. A continuous function is not always differentiable, but a differentiable function is always continuous.
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
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ample number of questions to practice Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : A continuous function is always differentiable.Reason : A differentiable function is always continuous.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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