Question

The tangent to the curve y = 2e^3x at the point (0, 2) meets the X-axis at ______.

Options

• (–3, 0)

• (3, 0)

• `(-1/3, 0)`

• `(1/3, 0)`

Answer 1

The tangent to the curve y = 2e^3x at the point (0, 2) meets the X-axis at `(- 1/3, 0)`.

Explanation:

y = 2e^3x

∴ `("d"y)/("d"x) = 6"e"^(3x)`

∴ `(("d"y)/("d"x))_((0, 2))` = 6

∴ Equation of the tangent at (0, 2) is

y – 2 = 6(x – 0)

⇒ y = 6x + 2

This tangent meets X-axis,

∴ y = 0

∴ 0 = 6x + 2 – x = ` -1/3`

∴ The required point is `(-1/3, 0)`.