Y1 Pure 12.1

Gradients of curves

Gradient of a straight line

Gradient of a curve

Y1 Pure 12.3

Differentiating x^n

Differentiate x^n, n a positive integer

Y1 Pure 12.5

Differentiating functions with 2 or more terms

Differentiating polynomials

Differentiating with fractional and negative indices

+G2-05 (dealing with indices)

Proof: sum rule for differentiation

Y1 Pure 12.7

Increasing and decreasing functions

Where functions are increasing/decreasing

Y1 Pure 12.9

Stationary points

Intro: stationary points

Examples of finding stationary points

Types of stationary points, part 1

+G3-14 (part 2)

Non-stationary points of inflection, example 1

Example 2

Example 3

+G3-22 (example 4)

Y1 Pure 12.11

Modelling with differentiation

Optimisation: rectangular fence problem

Optimisation: maximising volume of a box

Optimisation: maximising volume of a prism

Optimisation: minimising surface area of a box