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###### 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.... . . .. . . . . . .. . . . . .

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• ##### Piyush pachauri

Options C D are correct , Use Rolle's theorem

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

Sorry ,My bad. Use Rolle's theorem

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

and use Rolle's on all derivatives

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

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

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

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.

ok sir.. thank u sir for explanation..

is it clear or you have any doubt?

yes sir now its clear

• ##### Anonymous User Best Answer

check attachment D

and sir wont option c be true..?

by rolles theorem

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

sorry options D

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

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

ok understood sir ..

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

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

so f^n+1 is not constant

understand completely

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