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Proof for positivity? (1 Viewer)

adomad

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well u only need to prove it for 0<x<1 because, any number bigger than 1 will make the eqn positive as x^3 dominates...i may be wrong... im thinking of tangents to sinx curve to prove it but i am going no where
 

Lukybear

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Well Q says to prove using f'(x)>0 for x>0 and f(0) = 0

But f'(x) = x^2/3 +cosx-1
So mabey im thinking of proving x^2/3+cosx >1 for x>0
But how do i do that? Was thinking about graphing and showing it. But i think we need someform of higher formalised proof.
 

Lukybear

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O thxs. Thats very helpful. Would of never thought of that.
 

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