Equation of the tangent to the curve $y=

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

Equation of the tangent to the curve $y=e^{-|x|}$ at the point where it cuts the line x = 1

Options:

is ey + x = 2

is x + y = e

is ex + y = 1

does not exist

Correct Answer:

is ey + x = 2

Explanation:

$y=e^{-|x|}$ cut the line x = 1 at (1, 1/e)

$\left(\frac{d y}{d x}\right)_{(1,1 / e)}=\frac{-1}{e}$

Tangent $ y-\frac{1}{e}=-\frac{1}{e}(x-1)$

⇒ ey + x = 2