JEE Mains · Maths · STD 12 - 6. Application of derivatives
If \(m\) and \(n\) respectively are the number of local maximum and local minimum points of the function \(f ( x )=\int_{0}^{ x ^{2}} \frac{ t ^{2}-5 t +4}{2+ e ^{ t }} dt\), then the ordered pair \(( m , n )\) is equal to
- A \((3,2)\)
- B \((2,3)\)
- C \((2,2)\)
- D \((3,4)\)
Answer & Solution
Correct Answer
(B) \((2,3)\)
Step-by-step Solution
Detailed explanation
\(m = L \cdot \max\) \(N = L \cdot \min\) \(f(x)=\int\limits_{0}^{x^{2}} \frac{t^{2}-5 t+4}{2+e^{t}} d t\) \(f^{\prime}(x)=\frac{\left(x^{4}-5 x^{2}+4\right) 2 x}{2+e^{x^{2}}}=\frac{2 x\left(x^{2}-1\right)\left(x^{2}-4\right)}{2+e^{x^{2}}}\)…
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