Let ffunction in open interval (-r,r), when r>0.2times differentiable

There are two numbers M,N>0 so that |f ''(x)|<=N , |f(x)|<=M for all x in (-r,r).

Prove that |f ' (0) | <= 2sqrt(M*N) + 2*M/r

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- March 3rd 2010, 12:39 PMAlso sprach ZarathustraLandau inequality
Let f

function in open interval (-r,r), when r>0.*2*times differentiable

There are two numbers M,N>0 so that |f ''(x)|<=N , |f(x)|<=M for all x in (-r,r).

Prove that |f ' (0) | <= 2sqrt(M*N) + 2*M/r