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Solution for The Function F(X) = X2 E−X Is Monotonic Increasing When (A) X ∈ R − [0, 2] (B) 0 < X < 2 (C) 2 < X < ∞ (D) X < 0 - CBSE (Commerce) Class 12 - Mathematics

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Question

The function f(x) = x2 e−x is monotonic increasing when
(a) x ∈ R − [0, 2]
(b) 0 < x < 2
(c) 2 < x < ∞
(d) x < 0

Solution

(b) 0 < x < 2

\[f\left( x \right) = x^2 e^{- x} \]

\[f'\left( x \right) = 2x e^{- x} - x^2 e^{- x} \]

\[ = e^{- x} x\left( 2 - x \right)\]

\[\text { For f(x) to be monotonic increasing, we must have }\]

\[f'\left( x \right) > 0\]

\[ \Rightarrow e^{- x} x\left( 2 - x \right) > 0 \left[ \because e^{- x} > 0 \right]\]

\[ \Rightarrow x\left( 2 - x \right) > 0\]

\[ \Rightarrow x\left( x - 2 \right) < 0\]

\[ \Rightarrow 0 < x < 2\]

  Is there an error in this question or solution?

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Solution for question: The Function F(X) = X2 E−X Is Monotonic Increasing When (A) X ∈ R − [0, 2] (B) 0 < X < 2 (C) 2 < X < ∞ (D) X < 0 concept: Increasing and Decreasing Functions. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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