Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > If the functionin [2, 4] satisfies the Lagran...
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If the function 
in [2, 4] satisfies the Lagrange’s mean value theorem, then there exists some c ∈ [2, 4]. The value of c is
in [2, 4] satisfies the Lagrange’s mean value theorem, then there exists some c ∈ [2, 4]. The value of c is- a)12
- b)6
- c)√2
- d)√6
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If the functionin [2, 4] satisfies the Lagrange’s mean value the...
Concept:
Let f(x) is a function define on [a ,b] such that,
Let f(x) is a function define on [a ,b] such that,
- f(x) is a Continuous on [a , b]
- f(x) is Differentiable on [a , b]
Then, there exist a real number C ∈ (a , b) such that, According to Lagrangian Mean Value Theorem,
Calculation:
Given:
The function satisfies Lagrange's Mean Value Theorem that means it satisfies two condition given above 1 and 2
Therefore for the value of C we can write down above formula
Squaring on both sides,
3c2 - 12 = c2
2c2 = 12
c2 = 6
c = √6
Calculation:
Given:
The function satisfies Lagrange's Mean Value Theorem that means it satisfies two condition given above 1 and 2
Therefore for the value of C we can write down above formula
Squaring on both sides,
3c2 - 12 = c2
2c2 = 12
c2 = 6
c = √6
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If the functionin [2, 4] satisfies the Lagrange’s mean value theorem, then there exists some c ∈ [2, 4]. The value of c isa)12b)6c)√2d)√6Correct answer is option 'D'. Can you explain this answer?
Question Description
If the functionin [2, 4] satisfies the Lagrange’s mean value theorem, then there exists some c ∈ [2, 4]. The value of c isa)12b)6c)√2d)√6Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If the functionin [2, 4] satisfies the Lagrange’s mean value theorem, then there exists some c ∈ [2, 4]. The value of c isa)12b)6c)√2d)√6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the functionin [2, 4] satisfies the Lagrange’s mean value theorem, then there exists some c ∈ [2, 4]. The value of c isa)12b)6c)√2d)√6Correct answer is option 'D'. Can you explain this answer?.
If the functionin [2, 4] satisfies the Lagrange’s mean value theorem, then there exists some c ∈ [2, 4]. The value of c isa)12b)6c)√2d)√6Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If the functionin [2, 4] satisfies the Lagrange’s mean value theorem, then there exists some c ∈ [2, 4]. The value of c isa)12b)6c)√2d)√6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the functionin [2, 4] satisfies the Lagrange’s mean value theorem, then there exists some c ∈ [2, 4]. The value of c isa)12b)6c)√2d)√6Correct answer is option 'D'. Can you explain this answer?.
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