Doubt from application of derivatives


@Hari_Shankar sir , @Ajay_2021, @Samrat_2020

  • any shortcut for option c

  • I m getting abc kindly confirm that too

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I am getting a and b but don't know about c

@Jagdish_Singh sir

Can you tell me where did you find this problem please...
It's good

Is answer ABD
I get that f(x)=0 for all real x

I dont know but d cant be ans

Why f(x)=0 does satisfy

Ya f(x)=0 u will get its nano type function even as well as odd
The major doubt in option c is their any shortcut to do it..

Do you have a source for questions like these alongwith solutions . Pls provide as I face a problem in solving such questions

I dont know any source i m sorry someone asked mee problm

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@Ajay_2021 how u know this property just asking dnt mind it...

If possible proof the property