Question

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

Options

• (0, 1)

• `(- 1/2, 0)`

• (2, 0)

• (0, 2)

Answer 1

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

Explanation:

Equation of the curve is y = e^2x

Slope of the tangent `"dy"/"dx"` = 2e^2x

⇒ `"dy"/"dx"_(0, 1)` = 2 · e⁰ = 2

∴ Equation of tangent to the curve at (0, 1) is

y –1 = 2(x – 0)

⇒ y – 1 = 2x

⇒ y – 2x = 1

Since the tangent meets x-axis where y = 0

∴ 0 – 2x = 1

⇒ x = `(-1)/2`

So the point is `(- 1/2, 0)`.