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Question

If u(x) is larger of x(x3/6) and tan1x for 0<x1 then 48u(1/2) is equal to

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Solution

for0<x1f(x)=xx36f(0)=0f(x)=1x22>0f(1)=56g(x)=tan1xg(0)=0g(1)=π4andg(x)isalsoanincreasingfunctionin0<x1butπ4<56sofor0<x1f(x)islargerfunctionf(12)=234848f(12)=23

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