Calculus - APPLICATIONS OF DIFFERENTIATION

1. Calculus
How can we use algebra to model real world problems?
How can we use calculus to help us optimise real world problems?
Key words: gradient, derivative, function, differentiate
14 February 2023
>>>Challenge

2. Revision

3. Quadratic models: Applications

4. Quadratic models: Applications
1) Using GDC

5. Quadratic models: Applications
2) Algebraically

6. Calculus: optimisation
3) Using calculus

7. Calculus: Optimisation
Find the x coordinate of the local maximum

8. Calculus: Optimisation
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9. Calculus: Optimisation
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10. Calculus: Optimisation

11. Calculus: Optimisation

12. Calculus: Optimisation
𝑤𝑖𝑑𝑡ℎ = 12 − 2𝑥
𝑙𝑒𝑛𝑔𝑡ℎ = 12 − 2𝑥
Area = (12 − 2𝑥)(12 − 2𝑥)
ℎ𝑒𝑖𝑔ℎ𝑡 = 𝑥
= 144 − 48𝑥 + 4𝑥2
𝑉𝑜𝑙𝑢𝑚𝑒 = 144 − 48𝑥 + 4𝑥2 𝑥 = 144𝑥 − 48𝑥2 + 4𝑥3

13. Calculus: Optimisation
𝑣𝑜𝑙𝑢𝑚𝑒 = 144𝑥 − 48𝑥2 + 4𝑥3 𝑑𝑦
𝑑𝑥
= 144 − 96𝑥 + 12𝑥2
0 = 12(12 − 8𝑥 + 𝑥2)
0 = 12(𝑥 − 6)(𝑥 − 2)
𝑥 = 2 𝑥 = 6

14. Calculus: Optimisation

15. Calculus: Optimisation

16. Calculus: optimisation

17. Calculus: optimisation

18. Calculus: optimisation

19. Calculus: optimisation

20. Calculus: Optimisation

21. Calculus: Optimisation

22. Calculus: Optimisation

23. Quadratic models: Applications

24. Calculus: optimisation
3) Using calculus

26. Starter - Extension
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27. Revision