IB Maths AI 5.1 Definitions

This page contains our IB Maths AI definitions for 5.1. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Introduction to derivatives'.

All Topic 5 Sub-topics 5.1: Introduction To Derivatives 5.2: Applying Derivatives 5.3: Fundamentals Of Integration (HL)5.4: Advanced derivatives (HL)5.5: Further integration (HL)5.6: Applying integration (HL)5.7: Kinematics (HL)5.8: Introduction to differential equations (HL)5.9: Advanced differential equations

derivative

Measures how quickly a function changes; geometrically it gives the slope of the tangent to the curve, and in applications it represents an instantaneous rate of change.

gradient

The coefficient

a

y=ax+b

, giving the predicted change in

y

when

x

increases by

1

limit

The value that an expression approaches as the input approaches a specified number or tends to infinity, used to describe behaviour near a point or at an asymptote.

tangent

A line that touches a curve at a point and has the same local slope as the curve there, used to interpret the derivative at that point.

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