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Another form of Rolle’s theorem for the continuous condition is _____
- a)f is continuous on [a, a - h]
- b)f is continuous on [a, h]
- c)f is continuous on [a, a + h]
- d)f is continuous on [a, ah]
Correct answer is option 'C'. Can you explain this answer?
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Another form of Rolle’s theorem for the continuous condition is ...
's theorem is the Mean Value Theorem (MVT):
If f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:
f'(c) = (f(b) - f(a))/(b - a)
In other words, there exists a point c in the interval (a, b) where the slope of the tangent line to the curve f(x) is equal to the average rate of change of the function over the interval [a, b].
The Mean Value Theorem is a generalization of Rolle's theorem since it allows for the possibility that f(a) ≠ f(b). If f(a) = f(b), then the Mean Value Theorem reduces to Rolle's theorem.
The Mean Value Theorem is a powerful tool in calculus, as it provides a way to relate the behavior of a function over an interval to the behavior of its derivative at a specific point. It is used extensively in optimization problems and in proving other important theorems in calculus.
If f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:
f'(c) = (f(b) - f(a))/(b - a)
In other words, there exists a point c in the interval (a, b) where the slope of the tangent line to the curve f(x) is equal to the average rate of change of the function over the interval [a, b].
The Mean Value Theorem is a generalization of Rolle's theorem since it allows for the possibility that f(a) ≠ f(b). If f(a) = f(b), then the Mean Value Theorem reduces to Rolle's theorem.
The Mean Value Theorem is a powerful tool in calculus, as it provides a way to relate the behavior of a function over an interval to the behavior of its derivative at a specific point. It is used extensively in optimization problems and in proving other important theorems in calculus.
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Another form of Rolle’s theorem for the continuous condition is ...
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 continuous condition is _____a)f is continuous on [a, a - h]b)f is continuous on [a, h]c)f is continuous on [a, a + h]d)f is continuous on [a, ah]Correct answer is option 'C'. Can you explain this answer?
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Another form of Rolle’s theorem for the continuous condition is _____a)f is continuous on [a, a - h]b)f is continuous on [a, h]c)f is continuous on [a, a + h]d)f is continuous on [a, ah]Correct answer is option 'C'. 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 continuous condition is _____a)f is continuous on [a, a - h]b)f is continuous on [a, h]c)f is continuous on [a, a + h]d)f is continuous on [a, ah]Correct answer is option 'C'. 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 continuous condition is _____a)f is continuous on [a, a - h]b)f is continuous on [a, h]c)f is continuous on [a, a + h]d)f is continuous on [a, ah]Correct answer is option 'C'. Can you explain this answer?.
Another form of Rolle’s theorem for the continuous condition is _____a)f is continuous on [a, a - h]b)f is continuous on [a, h]c)f is continuous on [a, a + h]d)f is continuous on [a, ah]Correct answer is option 'C'. 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 continuous condition is _____a)f is continuous on [a, a - h]b)f is continuous on [a, h]c)f is continuous on [a, a + h]d)f is continuous on [a, ah]Correct answer is option 'C'. 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 continuous condition is _____a)f is continuous on [a, a - h]b)f is continuous on [a, h]c)f is continuous on [a, a + h]d)f is continuous on [a, ah]Correct answer is option 'C'. Can you explain this answer?.
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