Tangents and Normals (VCE SSCE Mathematical Methods): Flashcards

Line touching curve at one point with same slope as curve

Derivative gives gradient of tangent at that point

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

Line perpendicular to tangent at a point on curve

Product of gradients equals $-1$: $m_1 m_2 = -1$

$-\frac{1}{m}$ (negative reciprocal)

Point $(x_1, y_1)$ on curve and derivative $f'(x_1)$

Function continuous and $f'(x) \to \infty$ at that point

$f'(x) \to \infty$ from one side, $-\infty$ from other

Flip and flip the sign (reciprocal then negate)