Q90 / 150 · MHT CET 2021 (20 Sep Shift 1) · Mathematics

The equation of the tangent to curve $y=4 \mathrm{xe}^{\mathrm{x}}$ at $\left(-1, \frac{-4}{\mathrm{e}}\right)$ is

  • A
    $6 x-\frac{e}{4} y=-5$
  • B
    $\mathrm{x}-\frac{\mathrm{e}}{4} \mathrm{y}=0$
  • C
    $x=-1$
  • Correct answer
    D
    $y=\frac{-4}{e}$

Solution

$$ \begin{aligned} & y=4 \mathrm{x}^{\mathrm{x}} \\ & \therefore\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\left(-1, \frac{-4}{\mathrm{e}}\right)}=4(-1) \mathrm{e}^{-1}+4 \mathrm{e}^{-1}=\frac{-4}{\mathrm{e}}+\frac{4}{\mathrm{e}}=0 \end{aligned} $$ Thus tangent is parallel to $\mathrm{X}$ axis. Hence required equation of tangent is $y=\frac{-4}{e}$

Hence, the correct answer is option: 'D'.

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