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Consider f,g and h be three real valued differentiable functions defined on R.Let g(x)=x^(3)+g''(1)x^(3)+(3g'(1)-g''(1)-1)x+3g'(1) f(x)=xg(x)-12x+1 andf(x)=(h(x))^(2),where g(0)=1 The function y=f(x) has

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Exactly one local MINIMA and no local MAXIMA
Exactly one local maxima and no local minima
Exactly one local maxima and two local minima
Exactly two local maxima and no local minima

Answer :C


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