Question

The equation of the normal to the curve $y=e^x$ at $(0,1)$ is

• A. 2x + y = 1
• B. y - x = 1
• C. x + y = 1
• D. None of these

Answer 1

Answer: (C)

Given curve is $y=e^x\Rightarrow \frac{dy}{dx}=e^x$
Slope of normal $=\frac{-1}{e^x}$
$\therefore$ Slope of normal at point $(0,1)=\frac{-1}{e^0}=-1$
The equation of normal at $(0,1)$ is given by
$(y-1)=-1(x-0)$
$\Rightarrow x+y=1$