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

x + y = 1

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x - y = 1

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e y - x = e

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e (y - 1) + x = 0

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Solution

The correct option is A $x + y = 1$
$y = e^{x}$
$\frac{d y}{d x} = e^{x}$
$∴ {(\frac{d y}{d x})}_{(0, 1)} = 1 = m$ (say)
$∴$ Slope of normal at the given point is $= - \frac{1}{m} = - 1$
Therefore, the equation of normal is, $(y - 1) = - 1 (x - 0 \times a)$
$\Rightarrow x + y = 1$
Hence, option 'A' is correct.

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The equation of normal to the curve y=ex at the point (0,1) is -

The correct option is A x+y=1y=exdydx=ex∴(dydx)(0,1)=1=m (say)∴ Slope of normal at the given point is =−1m=−1Therefore, the equation of normal is, (y−1)=−1(x−0×a)⇒x+y=1Hence, option 'A' is correct.

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