Question

The equation of the tangent to the curve $y=e^{-|x|}$ at the point where the curves cuts the line x = 1 is

• A. x + y = e
• B. e(x + y) = 1
• C. y + ex = 1
• D. none of these

Answer 1

The correct option is D none of these

At $x=1,y=e^{-1}$,
$x=1>0\therefore y=e^{-x}$
$\frac{dy}{dx}=-e^{-x}\Rightarrow (\frac{dy}{dx}{)}_{x=1}=-\frac{1}{e}$
Equation, $y-e^{-1}=-\frac{1}{e}(x-1)$
$\Rightarrow ey-1=-x+1\Rightarrow x+ey=2$