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# Differentiation question watch

1. "A cylindrical can with height h metres and radius r metres has a capacity of 2 litres.
Find an expression for the surface area of the can in terms of r only."

I worked this out to be 2(pi)r^2 + 4.

The next part says "Find the value of r which minimises the surface area of the can."

I'm not even sure what that means. Do they want the smallest possible surface area? I also tried solving it like a quadratic, but it came up with a negative root.

Thanks in advance!
2. (Original post by JustJusty)
"A cylindrical can with height h metres and radius r metres has a capacity of 2 litres.
Find an expression for the surface area of the can in terms of r only."

I worked this out to be 2(pi)r^2 + 4.

The next part says "Find the value of r which minimises the surface area of the can."

I'm not even sure what that means. Do they want the smallest possible surface area? I also tried solving it like a quadratic, but it came up with a negative root.

Thanks in advance!
(assuming that's correct).

What's What happens when dA/dr = 0? You can then prove that it's a maximum or minimmum by checking the second derivative.
3. These types of questions are optimisation questions if you want to find explanations online somewhere. May be helpful if you're not sure what to search.
4. (Original post by B_9710)
These types of questions are optimisation questions if you want to find explanations online somewhere. May be helpful if you're not sure what to search.
inb4 he types 'optimisation problems' on Google and comes up with Lagrange multipliers and complex methods.
5. (Original post by JustJusty)
"A cylindrical can with height h metres and radius r metres has a capacity of 2 litres.
Find an expression for the surface area of the can in terms of r only."

I worked this out to be 2(pi)r^2 + 4.

The next part says "Find the value of r which minimises the surface area of the can."

I'm not even sure what that means. Do they want the smallest possible surface area? I also tried solving it like a quadratic, but it came up with a negative root.

Thanks in advance!
Differentiate your answer to part a) with respect to r, and put it = 0.

The best way to go about these questions is to imagine the SA and radius are on a graph, you want to find the turning point where the gradient is zero; you can assume this turning point is where r is highest and SA is lowest.

Find out the radius, and voila. If you happen to get two answers you can differentiate again to determine which is the minimum (in similar Qs).
6. (Original post by Zacken)
inb4 he types 'optimisation problems' on Google and comes up with Lagrange multipliers and complex methods.
Type A level then. Problem solved.
7. (Original post by Zacken)
(assuming that's correct).

What's What happens when dA/dr = 0? You can then prove that it's a maximum or minimmum by checking the second derivative.
Thanks you (again).
8. (Original post by JustJusty)
Thanks you (again).
No problemo!

In the future, if you have a physical quantity, let's say: the number of hours of sleep JustJusty can get, and you can represent that as a function of something else, say where is the age of your siblings, let's say - then you can optimise by looking for local minima or maxima.

That is, the optimal sleeping time occurs when your sibling is years old, where is a root of the equation. This 'optimal' can be either a minimum or a maximum and you can verify which one it is by checking the sign of .

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