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

Question

Angle between the tangents to the curve $y = {x^2} - 5x + 6$ at the points $(2,0)$ and $(3,0)$ is

Accepted Answer

$${{dy} \over {dx}} = 2x - 5$$

$$\therefore$$ $${m_1} = {\left( {2x - 5} \right)_{\left( {2,0} \right)}} =  - 1,$$

$${m_2} = {\left( {2x - 5} \right)_{\left( {3,0} \right)}} = 1 \Rightarrow {m_1}{m_2} =  - 1$$

i.e. the tangents are perpendicular to each other.

Solutions · 1