Tangents and Curves (Leaving Cert Mathematics): Flashcards

Touches curve at one point with same slope as curve

Slope of the tangent at any point $(x, y)$ on curve

Differentiate the function to find $\frac{dy}{dx}$

$y - y_1 = m(x - x_1)$

The slope of the line

The given point on the line

Parallel lines have equal slopes

Their slopes multiply to give $-1$

Set $\frac{dy}{dx}$ equal to that slope

Differentiate, substitute, apply point-slope form