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Deepak Patra posted an Question
November 19, 2021 • 11:45 am 30 points
  • IIT JAM
  • Mathematics (MA)

Differentiable supposef:rr isa function. then which the following statements are necessarilly frue? is (a.) if flx)sr<1 for alfer, then f has at least one fixed

differentiable Supposef:RR isa function. Then which the following statements are necessarilly frue? is (a.) If flx)sr<1 for alfeR, then f has at least one fixed point. * (b.) If f has a unique fixed point, then then S(x)sr<1 for all xeR-. (c.) If f has a unique fixed point, then f(x)2r>-i for all xeR (d.) None of these

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  • Anonymous User best-answer

    a and b

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    sir why not option c ... if we take f(x)= e^x it also satisfies f'(x) >r> -1 ?????

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    c also right I think 1 but in options -1

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    sir if we take f = x then .. f' (x)= 1 and and it does not follows the condition given in option 2

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    if u take f(x) =x then not unique fixed point. so we take not f(x)=x

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