Tangents and Normals

The tangent has the same gradient as the curve at the point of contact. The normal is perpendicular to the tangent.

• Tangent gradient: \(m_t=f'(a)\)
• Normal gradient: \(m_n=-\frac{1}{m_t}\), if \(m_t\ne0\)

Line equation

Through \((a,f(a))\), use \(y-y_1=m(x-x_1)\).