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Another form of Rolle’s theorem for the differential condition is _____
- a)f is differentiable on (a, ah)
- b)f is differentiable on (a, a - h)
- c)f is differentiable on (a, a/h)
- d)f is differentiable on (a, a + h)
Correct answer is option 'D'. Can you explain this answer?
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Another form of Rolle’s theorem for the differential condition i...
According to Rolle’s theorem, if f : [a,a+h] → R is a function such that
- f is continuous on [a,a + h]
- f is differentiable on (a,a + h)
- f(a) = f(a + h) then there exists at least one θ c ∈ (0,1) such that f’(a + θh) = 0
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Another form of Rolle’s theorem for the differential condition i...
Another form of Rolle's theorem is the generalized form of Rolle's theorem, also known as the Cauchy's mean value theorem.
The generalized form of Rolle's theorem states that if a function f(x) and its derivative g(x) are both continuous on the closed interval [a, b], and g(x) is non-zero at every point inside the open interval (a, b), then there exists at least one point c in (a, b) such that:
f'(c) = [f(b) - f(a)] / [g(b) - g(a)]
This form of Rolle's theorem is particularly useful when dealing with functions that have multiple roots or points where the derivative is zero. It allows us to find a point within the interval where the derivative of the function is equal to the average rate of change of the function over that interval.
The generalized form of Rolle's theorem states that if a function f(x) and its derivative g(x) are both continuous on the closed interval [a, b], and g(x) is non-zero at every point inside the open interval (a, b), then there exists at least one point c in (a, b) such that:
f'(c) = [f(b) - f(a)] / [g(b) - g(a)]
This form of Rolle's theorem is particularly useful when dealing with functions that have multiple roots or points where the derivative is zero. It allows us to find a point within the interval where the derivative of the function is equal to the average rate of change of the function over that interval.
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Another form of Rolle’s theorem for the differential condition is _____a)f is differentiable on (a, ah)b)f is differentiable on (a, a - h)c)f is differentiable on (a, a/h)d)f is differentiable on (a, a + h)Correct answer is option 'D'. Can you explain this answer?
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Another form of Rolle’s theorem for the differential condition is _____a)f is differentiable on (a, ah)b)f is differentiable on (a, a - h)c)f is differentiable on (a, a/h)d)f is differentiable on (a, a + h)Correct answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Another form of Rolle’s theorem for the differential condition is _____a)f is differentiable on (a, ah)b)f is differentiable on (a, a - h)c)f is differentiable on (a, a/h)d)f is differentiable on (a, a + h)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Another form of Rolle’s theorem for the differential condition is _____a)f is differentiable on (a, ah)b)f is differentiable on (a, a - h)c)f is differentiable on (a, a/h)d)f is differentiable on (a, a + h)Correct answer is option 'D'. Can you explain this answer?.
Another form of Rolle’s theorem for the differential condition is _____a)f is differentiable on (a, ah)b)f is differentiable on (a, a - h)c)f is differentiable on (a, a/h)d)f is differentiable on (a, a + h)Correct answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Another form of Rolle’s theorem for the differential condition is _____a)f is differentiable on (a, ah)b)f is differentiable on (a, a - h)c)f is differentiable on (a, a/h)d)f is differentiable on (a, a + h)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Another form of Rolle’s theorem for the differential condition is _____a)f is differentiable on (a, ah)b)f is differentiable on (a, a - h)c)f is differentiable on (a, a/h)d)f is differentiable on (a, a + h)Correct answer is option 'D'. Can you explain this answer?.
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