\( f(x) \) is a cubic polynomial such that \( f(3)=18, f(-1)=2 \) and \( f(x) \) has local maxim...

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\( f(x) \) is a cubic polynomial such that \( f(3)=18, f(-1)=2 \) and \( f(x) \) has local maximum at \( x=-1 \). If \( f^{\prime}(x) \) has local maximum at \( \mathrm{x}=0 \), then
(a) \( f(x) \) is increasing for \( x \in[1,2 \sqrt{5}] \)
(b) the distance between \( (-1,2) \) and \( (a, f(\mathrm{a})) \) where \( x=a \) is the point of local minimum is \( 2 \sqrt{5} \)
(c) \( f(x) \) has local minima at \( x=1 \)
(d) the value of \( f(0)=5 \)
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