IB Maths AI 5.2 Definitions

This page contains our IB Maths AI definitions for 5.2. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Applying 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

concavity

The way a graph curves; it is concave up where

f''(x)\gt0

and concave down where

f''(x)\lt0

inflexion

Describes a point where the graph changes concavity, which happens when $f''(x)$ changes sign (not just when $f''(x)=0$ ).

maximum

Describes a local highest point where the graph changes from increasing to decreasing; at a stationary point $x=c$ , this is indicated by $f''(c)\lt 0$ .

minimum

Describes a local lowest point where the graph changes from decreasing to increasing; at a stationary point $x=c$ , this is indicated by $f''(c)\gt 0$ .

normal

A line through a point on a curve that is perpendicular to the tangent at that point, with gradient equal to the negative reciprocal of the tangent gradient.

point-gradient

A form of a straight-line equation using a point

(x_1,y_1)

and gradient

m

y-y_1=m\left(x-x_1\right)

stationary point

Describes a point on a graph where the gradient is zero, so it occurs when $f'(x)=0$ .

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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