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What is the relation between f(a) and f(b) according to Rolle’s theorem?
- a)Equals to
- b)Greater than
- c)Less than
- d)Unequal
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
What is the relation between f(a) and f(b) according to Rolle’s ...
According to Rolle's theorem, if a function is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one point c in the open interval (a, b) where the derivative of the function is equal to zero, i.e., f'(c) = 0.
In other words, if a function satisfies the conditions of Rolle's theorem, it guarantees the existence of at least one point within the interval (a, b) where the derivative of the function is zero. However, it does not provide any information about the relationship between f(a) and f(b) specifically, other than the fact that they are equal.
In other words, if a function satisfies the conditions of Rolle's theorem, it guarantees the existence of at least one point within the interval (a, b) where the derivative of the function is zero. However, it does not provide any information about the relationship between f(a) and f(b) specifically, other than the fact that they are equal.
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What is the relation between f(a) and f(b) according to Rolle’s ...
According to Rolle’s theorem, if f : [a,b] → R is a function such that
- f is continuous on [a,b]
- f is differentiable on (a,b)
- f(a) = f(b) then there exists at least one point c ∈ (a,b) such that f’(c) = 0
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What is the relation between f(a) and f(b) according to Rolle’s theorem?a)Equals tob)Greater thanc)Less thand)UnequalCorrect answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What is the relation between f(a) and f(b) according to Rolle’s theorem?a)Equals tob)Greater thanc)Less thand)UnequalCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the relation between f(a) and f(b) according to Rolle’s theorem?a)Equals tob)Greater thanc)Less thand)UnequalCorrect answer is option 'A'. Can you explain this answer?.
What is the relation between f(a) and f(b) according to Rolle’s theorem?a)Equals tob)Greater thanc)Less thand)UnequalCorrect answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What is the relation between f(a) and f(b) according to Rolle’s theorem?a)Equals tob)Greater thanc)Less thand)UnequalCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the relation between f(a) and f(b) according to Rolle’s theorem?a)Equals tob)Greater thanc)Less thand)UnequalCorrect answer is option 'A'. Can you explain this answer?.
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