Question

The coordinates of the point on the curve y = 2x – x², the tangent at which has slope 4 are ______.

Options

• (–3, –1)

• (–1, –3)

• (1, 3)

• (–1, 3)

Answer 1

The coordinates of the point on the curve y = 2x – x², the tangent at which has slope 4 are (–1, –3).

Explanation:

∵ y = 2x – x²    ...(1)

∴ `dy/dx` = 2 – 2x

Slope of tangent = `dy/dx` = 2 – 2x

∴ 2 – 2x = 4   ....(Given)

∴ 2x = – 2,

∴ x = – 1

From (1): y = – 2 – 1 = – 3

∴ Point = (–1, –3)