Angle between the tangents to the curve `y=x^2-5x+6` at the points `(2,0) and (3,0)` is : (a) `pi/3` (b) `pi/2` (c) `pi/6` (d) `pi/4`

Explanation

Equation of given curve is,

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

So, `dy/dx = 2x-5`

We know at any point of curve slope of tangent of is `dy/dx`.

So, at `(2,0), dy/dx = m_1 = -1`

At `(3,0), dy/dx = m_2 = 1`

`:.m_1*m_2 = -1`

That means both these tangents are perpendicular.

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