Let \( f(x)=\left\{\begin{array}{cc}x^{3}-x^{2}+10 x-5, & x \leq 1 \\ -2 x+\log _{2}\left(b^{2}-...

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Let \( f(x)=\left\{\begin{array}{cc}x^{3}-x^{2}+10 x-5, & x \leq 1 \\ -2 x+\log _{2}\left(b^{2}-2\right), & x1\end{array}\right. \) the set of values of \( b \) for which \( f(x) \) have greatest value at \( x=1 \) is given by
(a) \( 1b \leq 2 \)
(b) \( b=\{14 \)
(c) \( b \in(-\infty,-1) \)
(d) \( [-\sqrt{130},-\sqrt{2}) \cup(\sqrt{2}, \sqrt{130}] \)
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