男人资源站-涩涩五月天-加勒比一区二区-欧美丰满少妇-清纯唯美亚洲-蜜臀久久99精品久久久久宅男-1024手机在线观看-a免费在线观看-日韩一区二区三免费高清在线观看-激情欧美一区二区-日韩综合网站-色小说av-夜夜夜操操操-色片在线播放-免费在线观看中文字幕

  • 翰林提供學(xué)術(shù)活動(dòng)、國(guó)際課程、科研項(xiàng)目一站式留學(xué)背景提升服務(wù)！
Home » 國(guó)際課程 » IB課程 » Details

IB DP Maths: AI SL復(fù)習(xí)筆記5.1.3 Modelling with Differentiation

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月19日 下午5:04

Modelling with Differentiation

What can be modelled with differentiation?

  • Recall that?differentiation?is about the?rate?of?change?of a function and provides a way of finding?minimum?and?maximum?values of a function
  • Anything that involves?maximising?or?minimising?a quantity can be modelled using differentiation; for example
    • minimising?the cost of raw materials in manufacturing a product
    • the?maximum?height a football could reach when kicked
  • These are called?optimisation?problems

What modelling assumptions are used in optimisation problems?

  • The quantity being?optimised?needs to be dependent on a?single?variable
    • If other variables are initially involved,?constraints?or?assumptions?about them will need to be made; for example
      • minimising the cost of the?main?raw material – timber in manufacturing furniture say – the cost of screws, glue, varnish, etc can be fixed or considered?negligible
    • Other?modelling?assumptions?may have to be made too; for example
      • ignoring air resistance and wind when modelling the path of a kicked football

How do I solve optimisation problems?

STEP 1

Rewrite the quantity to be optimised as a single variable, using any?constraints given in the question

 

?STEP 2
Use your GDC to find the (local) maximum or minimum points as required
Plot the graph of the function and use the graphing features of the GDC to?“solve for minimum/maximum” as required

 

?STEP 3
Note down the solution from your GDC and interpret the answer(s) in the context of the question

Exam Tip

  • The first part of rewriting a quantity as a single variable is often a “show that” question – this means you may still be able to access later parts of the question even if you can’t do this bit

Worked Example

A large allotment bed is being designed as a rectangle with a semicircle on each end, as shown in the diagram below.

5-1-3-ib-sl-ai-only-we-soltn-quest

5-1-3-ib-sl-ai-only-we-soltn-a

5-1-3-ib-sl-ai-only-we-soltn-b

5-1-3-ib-sl-ai-only-we-soltn-c

d)? ? ? ? Hence find the minimum perimeter.

5-1-3-ib-sl-ai-only-we-soltn-d

 

 

 

 

轉(zhuǎn)載自savemyexams

以上就是關(guān)于【IB DP Maths: AI SL復(fù)習(xí)筆記5.1.3 Modelling with Differentiation】的解答，如需了解學(xué)校/賽事/課程動(dòng)態(tài)，可至翰林教育官網(wǎng)獲取更多信息。

往期文章閱讀推薦：

深耕九載！30+國(guó)際競(jìng)賽/課程講義，碩博100%團(tuán)隊(duì)操刀，助力爬藤?zèng)_G5！

哈佛官方推薦書單曝光！原來普娃和藤校娃的差距還有閱讀！

? 2026. All Rights Reserved. 滬ICP備2023009024號(hào)-1

國(guó)際競(jìng)賽 國(guó)際競(jìng)賽
了解背提項(xiàng)目
國(guó)際課程 國(guó)際課程
國(guó)際課程
商務(wù)合作 商務(wù)合作
商務(wù)合作
課程試聽 課程試聽