Anku posted an Question
December 28, 2021 • 16:00 pm 30 points
  • IIT JAM
  • Mathematics (MA)

How to solve pls once show steps...

how to solve pls once show steps.... . . .. . . . . . .. . . . . .

2 Answer(s) Answer Now
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    Piyush pachauri best-answer

    Options C D are correct , Use Rolle's theorem

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    sir please can u once show how to apply mean value theorm for option c

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    Sorry ,My bad. Use Rolle's theorem

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    You can get it done using Rolle's as function is infinite diffrentiable f(0)=f(1) =0 so there exists c in (0,1) such f'(c) =0

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    and use Rolle's on all derivatives

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    sir below navdeep sir has explained we cant use rolles theorem he gave following explanation

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    f(0)=f(1)= 0 there exist c€(0,1) f'(c)=0 but it is not necessary f"(c)=0

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    sir can u please tell if above explanation is correct or not..

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    sir kindly reply..

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    I was checking Navdeep sir's comment , He has given you wrong example because his example does not satisfy the condition of f'(0)=0 so f'' was not zero at any point.

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    ok sir.. thank u sir for explanation..

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    is it clear or you have any doubt?

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    yes sir now its clear

  • Anonymous User Best Answer

    check attachment D

    cropped6236527209190468153.jpg
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    and sir wont option c be true..?

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    by rolles theorem

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    f(0)=f(1)= 0 there exist c€(0,1) f'(c)=0 but it is not necessary f"(c)=0

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    sorry options D

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    sir can u give an example if possible when f" (c)≠0

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    f(x)=x(x-1) ;f'(x)=2x-1=0 when x=1/2 but f"(x)≠0

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    ok understood sir ..

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    sir last doubt if fⁿ+¹(x)=0 so is not this a constant..and so should not a be true..?

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    a not true bcz f^(n+1)(x) =0 for any value but not all value

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    so f^n+1 is not constant

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    understand completely

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