JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the absolute maximum value of the function \(f ( x )\) \(=\left( x ^{2}-2 x +7\right) e ^{\left(4 x^{3}-12 x ^{2}-180 x +31\right)}\) in the interval \([-3\), \(0]\) is \(f (\alpha)\), then.
- A \(\alpha=0\)
- B \(\alpha=-3\)
- C \(\alpha \in(-1,0)\)
- D \(\alpha \in(-3,-1)\)
Answer & Solution
Correct Answer
(B) \(\alpha=-3\)
Step-by-step Solution
Detailed explanation
\(f^{\prime}(x)=e^{\left(4 x^{2}-12 x^{2}-180 x+31\right)}(12\left(x^{2}-2 x+7\right)\) \((x+3)(x-5)+2(x-1)\) for \(x \in[-3,0]\) \(f ^{\prime}( x )<0\) \(f ( x )\) is decreasing function on \([-3,0]\) The absolute maximum value of the function \(f(x)\) is at \(x=-3\)…
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