Question

The equation of the tangent to the curve f (x) = 1 + e^–2x where it cuts the line y = 2 is

• A. x + 2y = 2
• B. 2x + y = 2
• C. x – 2y = 1
• D. x – 2y + 2 = 0

Answer 1

Answer: (B)

2x + y = 2

Answer 2

When y =2, e^–2x = 1 ⇒ x = 0,

and$\frac{df}{dx}$ = –2e^–2x ⇒ $\left. \ \frac{df}{dx} \right|_{x = 0}$= –2

⇒ The equation of the tangent is, (y –2) = –2 (x – 0)

⇒ 2 x + y – 2 = 0