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NBHM PhD Screening Test 2005 Analysis

What is the least value of $K>0$ such that $|\sin^2x-\sin^2y|≤K|x-y|$ $\forall$ $x$,$y \in \mathbb R$

How can I solve this problem?

  • 0
    Find $\max_x |(\sin^2)'(x)|$ (its $1$!).2012-12-31
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    @copper.hat: Is this fact useful: by the mean value we have $|\sin(x)-\sin(y)|\leq |x-y|$?2012-12-31
  • 0
    @BabakSorouh: I don't think so, but there is a simple way of calculating the $K$ for differentiable functions.2012-12-31

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