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onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ R
Statement -1 : f ' ( 4) = 0
Statement -2 : f is continous in [2, 5], differentiable in (2, 5) and f ( 2) = f ( 5)
- a)Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for statement-1.
- b)Statement -1 is true, Statement -2 is false
- c)Statement -1 is false, Statement -2 is true.
- d)Statement-2 is a correct explanation for Statement -1.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ RStateme...
f (x ) is constant is [2, 5]
Most Upvoted Answer
onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ RStateme...
Explanation:
Statement 1: f(4) = 0
- To find f(4), we substitute x = 4 into the given function f(x) = |x - 2| + |x - 5|
- f(4) = |4 - 2| + |4 - 5| = 2 + 1 = 3, not 0
- Therefore, Statement 1 is false.
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5)
- The function f(x) = |x - 2| + |x - 5| is continuous in the closed interval [2, 5] as it is a sum of two continuous functions.
- The function is also differentiable in the open interval (2, 5) as it is composed of linear functions.
- However, f(2) = |2 - 2| + |2 - 5| = 0 + 3 = 3, and f(5) = |5 - 2| + |5 - 5| = 3 + 0 = 3
- Since f(2) is not equal to f(5), Statement 2 is false.
Therefore, the correct answer is option A where Statement 1 is false, Statement 2 is false, and Statement 2 is not a correct explanation for Statement 1.
Statement 1: f(4) = 0
- To find f(4), we substitute x = 4 into the given function f(x) = |x - 2| + |x - 5|
- f(4) = |4 - 2| + |4 - 5| = 2 + 1 = 3, not 0
- Therefore, Statement 1 is false.
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5)
- The function f(x) = |x - 2| + |x - 5| is continuous in the closed interval [2, 5] as it is a sum of two continuous functions.
- The function is also differentiable in the open interval (2, 5) as it is composed of linear functions.
- However, f(2) = |2 - 2| + |2 - 5| = 0 + 3 = 3, and f(5) = |5 - 2| + |5 - 5| = 3 + 0 = 3
- Since f(2) is not equal to f(5), Statement 2 is false.
Therefore, the correct answer is option A where Statement 1 is false, Statement 2 is false, and Statement 2 is not a correct explanation for Statement 1.
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onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ RStatement -1 : f ' ( 4) = 0Statement -2 : f is continous in [2, 5], differentiable in (2, 5) and f ( 2) = f ( 5)a)Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for statement-1.b)Statement -1 is true, Statement -2 is falsec)Statement -1 is false, Statement -2 is true.d)Statement-2 is a correct explanation for Statement -1.Correct answer is option 'A'. Can you explain this answer?
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onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ RStatement -1 : f ' ( 4) = 0Statement -2 : f is continous in [2, 5], differentiable in (2, 5) and f ( 2) = f ( 5)a)Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for statement-1.b)Statement -1 is true, Statement -2 is falsec)Statement -1 is false, Statement -2 is true.d)Statement-2 is a correct explanation for Statement -1.Correct answer is option 'A'. 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 onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ RStatement -1 : f ' ( 4) = 0Statement -2 : f is continous in [2, 5], differentiable in (2, 5) and f ( 2) = f ( 5)a)Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for statement-1.b)Statement -1 is true, Statement -2 is falsec)Statement -1 is false, Statement -2 is true.d)Statement-2 is a correct explanation for Statement -1.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ RStatement -1 : f ' ( 4) = 0Statement -2 : f is continous in [2, 5], differentiable in (2, 5) and f ( 2) = f ( 5)a)Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for statement-1.b)Statement -1 is true, Statement -2 is falsec)Statement -1 is false, Statement -2 is true.d)Statement-2 is a correct explanation for Statement -1.Correct answer is option 'A'. Can you explain this answer?.
onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ RStatement -1 : f ' ( 4) = 0Statement -2 : f is continous in [2, 5], differentiable in (2, 5) and f ( 2) = f ( 5)a)Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for statement-1.b)Statement -1 is true, Statement -2 is falsec)Statement -1 is false, Statement -2 is true.d)Statement-2 is a correct explanation for Statement -1.Correct answer is option 'A'. 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 onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ RStatement -1 : f ' ( 4) = 0Statement -2 : f is continous in [2, 5], differentiable in (2, 5) and f ( 2) = f ( 5)a)Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for statement-1.b)Statement -1 is true, Statement -2 is falsec)Statement -1 is false, Statement -2 is true.d)Statement-2 is a correct explanation for Statement -1.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for onsider the function, f ( x ) =| x - 2 | + | x - 5 | .x∈ RStatement -1 : f ' ( 4) = 0Statement -2 : f is continous in [2, 5], differentiable in (2, 5) and f ( 2) = f ( 5)a)Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for statement-1.b)Statement -1 is true, Statement -2 is falsec)Statement -1 is false, Statement -2 is true.d)Statement-2 is a correct explanation for Statement -1.Correct answer is option 'A'. Can you explain this answer?.
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