JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f(x)=\left\{\begin{array}{cc}x^{3}-x^{2}+10 x-7, & x \leq 1 \\ -2 x+\log _{2}\left(b^{2}-4\right), & x>1\end{array}\right.\) 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 \([-\sqrt{6},-2) \cup(2, \sqrt{6}]\)
Answer & Solution
Correct Answer
(C) \([-6,-2) \cup(2,6]\)
Step-by-step Solution
Detailed explanation
\(f(1)=3\) For \(x <1, f ^{\prime}( x )=3 x ^{2}-2 x +10>0\) \(\Rightarrow f ( x )\) is increasing For \(x >1, f ^{\prime}( x )<0\) function is decreasing. \(\lim _{x \rightarrow 1^{+}} f(x)=-2+\log _{2}\left(b^{2}-4\right)\) For maximum value at \(x=1\)…
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