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A function increases where dy/dx > 0 and decreases where dy/dx < 0. This topic uses differentiation to find the intervals on which a function increases or decreases. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Differentiate, then solve the inequality for where the derivative is positive to find increasing intervals, and negative for decreasing. For a cubic the derivative is a quadratic, so factorise it, find where it crosses zero and sketch the parabola to read off which side is which.
Before you start
You will want basic differentiation and inequalities at your fingertips first. It underpins curve sketching. This sits in Pure 2.
What you learn
The course works through the sign of the gradient, decreasing intervals of a cubic, increasing intervals of a cubic and linking to turning points. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Increasing & Decreasing Functions as one of the Differentiation topics in our A-level course library, at the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Related topics students usually take next include Parametric Differentiation, Product Rule and Quotient Rule. For unlimited practice, the Differentiation revision engine builds new questions on demand and records your accuracy.
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