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

What is a tangent to a curve at a point?

A line that touches the curve at one point only.

What does the gradient of a curve represent?

The gradient of its tangent at that point.

How to find the equation of a tangent?

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

What is the normal line at a point on a curve?

A line perpendicular to the tangent at that point.

How to calculate the gradient of a normal?

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

What is the formula for a line given a point and gradient?

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

What is the first step to find the tangent at $x = 1$?

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

How to find coordinates of the point on a curve?

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

How do you find the normal line of $y=4x^2+x-3$ at $x=2$?

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

How do you confirm if critical points are maxima/minima?

Use the second derivative test or sign change method.