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 \( h(0)=1 \)
The function \( y=f(x) \) has
(a) Exactly one local minima and no local maxima
(b) Exactly one local maxima and no local minima
(c) Exactly one local maxima and two local minima
(d) Exactly two local maxima and one local minima
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