Calculus Practice Problem – Differentiation, speed-distance-time and Minimization

https://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011mmcas2-w.pdf

2011 VCAA Mathematical Methods Unit 3&4 Exam 2 Q4 Tasmania Jones Max Min Problem – This question is worth 18 marks and should take you approximately 20-25 minutes to complete.

0:00 part a
6:17 part b
14:55 part c
23:20 part d
28:49 part e
33:29 part f

See below for some Hints:

part a: Distance between two points means think Pythagoras’ theorem
part c: speed=distance/time
part d: minimum time means derivative = 0
part f: the key idea with part f is that as k becomes very big (with x less than or equal to sqrt7/2) it takes longer to travel along the river (time overall goes up), which means travelling straight to desalination plant is best. The other key idea is that for a minimum to occur we need to consider the derivative and in this case the derivative depends on the k value AND we consider the derivative when x=sqrt7/2

Questions?

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