Gradients, Tangents & Normals (Edexcel A-Level Mathematics): Flashcards

A line that touches the curve at one point only.

The gradient of its tangent at that point.

Use point and gradient in $y - y_1 = m(x - x_1)$.

A line perpendicular to the tangent at that point.

It is the negative reciprocal of the tangent's gradient.

$y - y_1 = m(x - x_1)$, where $m$ is the gradient.

Find the gradient function, $dy/dx$, of the curve.

Substitute $x$ into the curve equation to get $y$.

1. Find slope of tangent. 2. Use negative reciprocal for normal.

Use the second derivative test or sign change method.