Question

If the tangent to the curve y = 3x² - 2x + 1 at a point Pis parallel toy = 4x + 3, the co-ordinates of P are

Options

• (2, 1)

• (1, 2)

• (-1, 2)

• (2, -1)

Answer 1

(1, 2)

Explanation:

Let the coordinates of P be (x₁, y₁)

Then, `"y"_1 = 3x_1^2 - 2x_1 + 1`  ...(i)

Now, y = 3x² - 2x + 1

∴ `"dy"/"dx" = 6x - 2`

∴ `("dy"/"dx")_(("x"_1;"y"_1))` = 6x₁ - 2

Slope of the given line is 4.

Since the tangent is parallel to the given line,

slope of the tangent = 4

`=> 6x<sub>1</sub> - 2 = 4`

`=> x_1 = 1`

From (i), y₁ = 2

∴ The coordinates of P are (1, 2)