Question

The equation of the tangent to the curve y = `2x + 1/x^2`, that is parallel to the X-axis, is ______.

Options

• y = 2

• y = 3

• y = 0

• y = 1

Answer 1

The equation of the tangent to the curve y = `2x + 1/x^2`, that is parallel to the X-axis, is y = 3.

Explanation:

Let (x₁, y₁) be a point on the curve y = 2x + `1/x^2`.

Since the tangent is parallel to X-axis,

`("dy"/"dx")_((x_1, "y"_1)) = 0 ⇒ 2 - 2/x_1^3 = 0 => x_1 = 1`

Now, `"y"_1 = 2x_1 + 1/x_1^2`

`=> "y"_1 = 2 + 1`

`=> "y"_1 = 3`

∴ equation of the tangent at (1, 3) is

y - 3 = 0 ⇒ y = 3