[RESOLVED] Problem with Differentiation

1. A ship is to make a voyage of 200km at a constant speed. When the speed of the ship is v km/h the cost is £(v² + 4000/v) per hour. Find the speed at which the ship should travel so that the cost of the voyage is a minimum.


I was trying hard to figure out how to solve this question, sadly I dont even know where to start and how to start... Please help... :cry:

2. An open cylindrical wastepaper bin, of radius r cm and capacity V cm³, is to have a surface area of 5000 cm². Show that V = 1/2r(5000-πr²)

For this 2nd question, I have faint idea on how to do it, but I don't know how am I suppose to show my answer...

1. Let C = v^2 + 4000v^-1

Find dC/dv

Solve dC/dv = 0

2. Let cylinder have radius r and height h
Surface area of cylinder = πr² + 2πrh = 5000

2πrh = 5000 - πr²

h = (1/2πr)(5000 - πr²)

V = πr²h = πr²(1/2πr)(5000 - πr²) = 1/2r(5000-πr²)

Yay finally I know how to show my answer! Thanks :bigyello:

No problem

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