Question:
If $f (x) = xe^{x(1-x)}$ , then f (x) is
If $f (x) = xe^{x(1-x)}$ , then f (x) is
Updated On: Aug 23, 2023
- increasing on [-1/2, 1]
- decreasing on R
- increasing on R
- decreasing on [-1/2, 1]
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The Correct Option is A
Solution and Explanation
The correct option is(A): increasing on [-1/2, 1]
\(f (x) = xe^{x (1 - x)}\)
\(\Rightarrow \, f'(x) = e^{x (1-x)} + (1 - 2x) x e^{x (1-x)}\)
\(= - e^{x (1-x) } (2x^2 - x - 1) = - e^{x (1 - x) } (2x + 1) (x - 1)\)
\(\therefore\) f (x) is increasing on [-1/2, 1]
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