From 364ce84e8a8306fb428146dc372afe3d30672351 Mon Sep 17 00:00:00 2001 From: eggy Date: Fri, 20 Nov 2020 19:51:31 -0500 Subject: [PATCH] math: add optimisation --- docs/mhf4u7.md | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/docs/mhf4u7.md b/docs/mhf4u7.md index 200b0c9..acfc874 100644 --- a/docs/mhf4u7.md +++ b/docs/mhf4u7.md @@ -602,6 +602,17 @@ Changes in concavity only occur at points of inflection. A cusp is a point on a continuous function that is not differentiable as the slopes on both sides approach -∞ and ∞. Concavity does not change at a cusp, but they may be considered for local extrema. +### Optimisation + +To optimise for a maximum or minimum of a variable: + + - Identify an equation with only one variable dependent on another + - Find the first derivative and identify critical points + - Use the second derivative test to identify if the critical point is a maximum or minimum + - Check constraints and throw away any inadmissible results + +Diagrams with labelled variables may be helpful. + ## Resources - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)