Question

The equation of the tangent to the curve y = x² + 4x + 1 at P(−1, −2) is ______.

Options

• 2x − y = 0

• x + 2y + 5 = 0

• 2x + 4 = 3y

• 5x + y = 1

Answer 1

The equation of the tangent to the curve y = x² + 4x + 1 at P(−1, −2) is 2x − y = 0.

Explanation:

y = x² + 4x + 1 at (−1, −2)

Given the equation of the curve is y = x² + 4x + 1

Differentiating w.r.t. x

`dy/dx = 2 x + 4`

`(dy/dx)_ (at(-1,-2))` = 2(−1) + 4 = 2

∴ Slope of the tangent at the point (−1, −2) = 2

∴ The equation of the tangent at point  (−1, −2) is

y − (−2) = 2[x − (−1)]

2x − y = 0