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Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f ‘ (x) = 0 for every x, then
  • a)
    f is constant function if f  1/2 = f (3)
  • b)
    f is a constant function
  • c)
    f is a constant function if f  1/2 = 0
  • d)
    f is not a constant function
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let f be a real valued function defined on (0, 1)∪ (2, 4) such tha...
f ‘ (x) = 0 ⇒ f (x)is constant in (0 , 1)and also in (2, 4). But this does not mean that f (x) has the same value in both the intervals . However , if f (c) = f (d) , where c ∈ (0 , 1) and d ∈ (2, 4) then f (x) assumes the same value at all x ∈ (0 ,1) U (2, 4) and hence f is a constant function.
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Most Upvoted Answer
Let f be a real valued function defined on (0, 1)∪ (2, 4) such tha...
Okay, f is a real valued function defined on the open interval (0, 1).
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Community Answer
Let f be a real valued function defined on (0, 1)∪ (2, 4) such tha...
I think it has to be option B

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Let f be a real valued function defined on (0, 1)∪ (2, 4) such that f ‘ (x) = 0 for every x, thena)f is constant function if f 1/2=f (3)b)f is a constant functionc)f is a constant function if f 1/2= 0d)f is not a constant functionCorrect answer is option 'A'. Can you explain this answer?
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