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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=x^2 e^{-x}$ is monotonic increasing when :
  • A
    $\text{x}\in\text{R}-[0,2]$
  • ✓
    $0 < \text{x} < 2$
  • C
    $2 < \text{x} < \infty$
  • D
    $\text{x} < 0$
✓

Answer

Correct option: B.
$0 < \text{x} < 2$
$f(x)=x^2 e^{-x}$
$\Rightarrow f^{\prime}(x)=-x^2 e^{-x}+2 x e^{-x}$
$\Rightarrow f^{\prime}(x)=-e^{-x} x(x-2)$
Given that function is monotonically increasing.
$-e^{-x} x(x-2) > 0$
$x(x-2) < 0$
$0$

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