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Let f defined on [0, 1] be twice diffe...

Let `f` defined on `[0, 1]` be twice differentiable such that `| f"(x)| <=1` for `x in [0,1]`. if `f(0)=f(1)` then show that `|f'(x)<1` for all `x in [0,1]`.

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CENGAGE-APPLICATION OF DERIVATIVES-Solved Examples And Exercises
  1. Let f defined on [0, 1] be twice differentiable such that | f"(x)| ...

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  2. The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0

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  6. Find the value of a if the curves (x^2)/(a^2)+(y^2)/4=1a n dy^3=16 x c...

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  8. In the curve x^(m+n)=a^(m-n)y^(2n) , prove that the m t h power of the...

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  14. Let 0<a<b<pi/2dotIff(x)=|tanxtanatanbsinxsinasinbcosxcosacosb|,t h e n...

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  16. Prove that if 2a0 2<15 a , all roots of x^5-a0x^4+3a x^3+b x^2+c x+d=0...

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  18. Prove that |tan^(-1)x-tan^(-1)y|lt=|x-y|AAx , y in Rdot

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  20. If a &gt; b &gt;0, with the aid of Lagranges mean value theorem, prov...

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