JEE Mains · Maths · STD 12 - 6. Application of derivatives
The function \(f ( x )= xe x ^{ x (1- x )}, x \in R\), is
- A increasing in \(\left(-\frac{1}{2}, 1\right)\)
- B decreasing in \(\left(\frac{1}{2}, 2\right)\)
- C increasing in \(\left(-1,-\frac{1}{2}\right)\)
- D decreasing in \(\left(-\frac{1}{2}, \frac{1}{2}\right)\)
Answer & Solution
Correct Answer
(A) increasing in \(\left(-\frac{1}{2}, 1\right)\)
Step-by-step Solution
Detailed explanation
\(f(x)=x e^{x(1-x)}\) \(f^{\prime}(x)=-e^{x(1-x)}(2 x+1)(x-1)\) \(f ( x )\) is increasing in \(\left(-\frac{1}{2}, 1\right)\)
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