Question

The slope of tangent at any point on the curve is 3. lf the curve passes through (1, 1), then the equation of curve is ______.

Options

• y = 3x – 2

• y = 3x + 2

• y = 2x – 3

• y = 2x + 3

Answer 1

The slope of tangent at any point on the curve is 3. lf the curve passes through (1, 1), then the equation of curve is y = 3x – 2.

Explanation:

Let the equation of the curve be y = f(x)

∴ Slope of tangent at any point (x, y) is `dy/dx`

∴ `dy/dx` = 3   ....(Given)

∴ dy = 3 dx

∴ `int dy = 3 int dx`

∴ y = 3x + c

This passes through (1, 1)

∴ 1 = 3 + c

∴ c = – 2

∴ y = 3x – 2