Tangents and Normals

Equation of a Tangent

The tangent to a curve $y = f(x)$ at a point $(x_1, y_1)$ has slope $f'(x_1)$:

$$y - y_1 = f'(x_1)(x - x_1)$$

Equation of a Normal

The normal is perpendicular to the tangent, with slope $-\dfrac{1}{f'(x_1)}$.