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Sagot :

On a f(x)= x^2/2-x^2e^x-1. 
f'(x)=2x/2-2x*e^(x-1)-x²*e^(x-1)
     =x-(x²+2x)*e^(x-1)
     =x(1-(x+2)*e^(x-1))
     =x*g(x)

avec g(x)=1-(x+2)*e^(x-1)

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