Consider \( f \), \( g \) and \( h \) be three real valued differentiable functions defined on \...

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Consider \( f \), \( g \) and \( h \) be three real valued differentiable functions defined on \( R \).
Let \( g(x)=x^{3}+g^{\prime \prime}(1) x^{2}+\left(3 g^{\prime}(1)-g^{\prime \prime}(1)-1\right) x+3 g^{\prime}(1) \) \( f(x)=x g(x)-12 x+1 \)
and \( f(x)=(h(x))^{2} \), where \( h(0)=1 \).
Which one of the following does not hold good for \( y=h(x) ? \)
(a) Exactly one critical point
(b) No point of inflexion
(c) Exactly one real zero in \( (0,3) \)
(d) Exactly one tangent parallel to \( X \)-axis
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