Calculus

AdvancedMaths revision

Applications of Derivatives

Use derivatives to optimise, approximate and analyse motion and graph behaviour.

Open calculator

Focus points

✓Optimise quantities under constraints.

✓Use derivative signs for graph behaviour.

✓Apply tangent and rate models.

orin

Orin

The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions

Question 1FluencyCore

Original practice · Free Online Revision

Skill · increasing/decreasing

Find intervals where f(x)=x³−3x²−9x+1 is increasing.

Question 2FluencyCore

Original practice · Free Online Revision

Skill · classification

Classify stationary points of f(x)=x³−3x.

Question 3FluencyCore

Original practice · Free Online Revision

Skill · tangent

Find the tangent to y=x²+2x at x=3.

Question 4ApplicationCore

Original practice · Free Online Revision

Skill · optimisation

A rectangle has perimeter 40 m. Find dimensions giving maximum area.

Question 5ApplicationCore

Original practice · Free Online Revision

Skill · modelling

An open-top box is made by cutting squares of side x from corners of a 20 cm by 14 cm sheet. Write volume V(x).

Question 6ChallengeStretch

Original practice · Free Online Revision

Skill · optimisation

For the box above, find the critical points numerically/exactly enough to identify the maximizing x.

Question 7ApplicationStretch

Original practice · Free Online Revision

Skill · linear approximation

Use linear approximation at x=4 to estimate √4.1.

Question 8ChallengeStretch

Original practice · Free Online Revision

Skill · related rates

A spherical balloon radius increases at 2 cm/s. Find dV/dt when r=5 cm.