The abscissa of the point on the curve $y=\mathrm{a}\left(\mathrm{e}^{\frac{x}{a}}+\mathrm{e}^{-\frac{x}{a}}\right)$ where the tangent is parallel to the X -axis is
0
a
2 a
-2 a
Solution
$\begin{aligned}
& \quad y=\mathrm{a}\left(\mathrm{e}^{\frac{x}{a}}+\mathrm{e}^{\frac{-x}{a}}\right) \\
& \therefore \quad \frac{\mathrm{d} y}{\mathrm{~d} x}=\mathrm{e}^{\frac{x}{a}}-\mathrm{e}^{-\frac{x}{a}}
\end{aligned}$ Since the tangent is parallel to X -axis, $\frac{\mathrm{d} y}{\mathrm{~d} x}=0$
$\begin{aligned}
& \Rightarrow \mathrm{e}^{\frac{x}{\mathrm{a}}}-\mathrm{e}^{-\frac{x}{\mathrm{a}}}=0 \\
& \Rightarrow \mathrm{e}^{\frac{2 x}{\mathrm{a}}}=0 \\
& \Rightarrow x=0
\end{aligned}$