The equation of the tangent to the curve f(x) = 1 + e–2x where it cuts the line y = 2 is
Answer & explanation
Correct answer: option 2
When y = 2, e–2x = 1 ⇒ x = 0,
and $\frac{df}{dx} = -2e^{-2x} ⇒ \frac{df}{dx}|_{x=0} = - 2$
⇒ The equation of the tangent is, (y - 2) = - 2 (x - 0) ⇒ 2 x + y - 2 = 0.
Hence (B) is the correct answer.