Let \( f(x)=\left\{\begin{array}{cc}x^{3}-x^{2}+10 x-7, & x \leq 1 \\ -2 x+\log _{2}\left(b^{2}-... VIDEO
Let \( f(x)=\left\{\begin{array}{cc}x^{3}-x^{2}+10 x-7, & x \leq 1 \\ -2 x+\log _{2}\left(b^{2}-4\right), & x1\end{array}\right. \)
Then the set of all values of \( b \), for which \( f(x) \) has maximum value at \( x=1 \), is
(a) \( (-6,-2) \)
(b) \( (2,6) \)
(c) \( [-6,-2) \cup(2,6] \)
(d) \( [-\sqrt{6},-2] \cup(2, \sqrt{6}] \)
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