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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

ConceptIncreasing and Decreasing Functions

#### 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?

#### Video TutorialsVIEW ALL [3]

Solution 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.
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