Question

The angle between the tangents to the curve y = `x^2 - 5x + 6` at the points (2, 0) and (3, 0) is ______ 

Options

• `pi/3`

• `pi/2`

• `pi/6`

• `pi/4`

Answer 1

The angle between the tangents to the curve y = `x^2 - 5x + 6` at the points (2, 0) and (3, 0) is `underline(pi/2)`. 

Explanation:

y = `x^2 - 5x + 6`

∴ `dy/dx = 2x - 5`

∴ `(dy/dx)_{(2, 0)} = 2(2) - 5 = -1 = "m"_1` (say)

and `(dy/dx)_{(3, 0)} = 2(3) - 5 = 1 = "m"_2` (say)

Here, m₁ m₂ = -1

∴ The required angle is `pi/2`.