The equation of the tangent to curve $y=4 \mathrm{xe}^{\mathrm{x}}$ at $\left(-1,…
The equation of the tangent to curve $y=4 \mathrm{xe}^{\mathrm{x}}$ at $\left(-1, \frac{-4}{\mathrm{e}}\right)$ is
- $6 x-\frac{e}{4} y=-5$
- $\mathrm{x}-\frac{\mathrm{e}}{4} \mathrm{y}=0$
- $x=-1$
- $y=\frac{-4}{e}$
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 $y=\frac{-4}{e}$
Asked in: MHT CET 2021 (20 Sep Shift 1)
Practice more Applications of Derivatives questions on Aicharya