Cone volume differentiation to find maximum value

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If all understanding should fail, don't bother. Simply stick to r=4/3. It'll do, for now. Use that value to calculate the max volume, it's all the question ever really wanted.

Reply 21

Zacken

Original post by Bath_Student

keep quiet if you're don't know what you're on about.

You keep quiet.

r=0

means that the RADIUS IS ZERO. Try and wrap your head around this. A radius of zero will not yield a maximum volume.

Reply 22

Bath_Student

Original post by Zacken

"I art better than thou."

You absolute plonker. r=0 would be a perfectly feasible answer, if it weren't out of our man-made domain. OP needs to understand the general method for these problems.

Reply 23

Bath_Student

Original post by Zacken

Also, where's the display picture? Have we lost confidence in our "attractiveness"?

Reply 24

Zacken

Original post by Bath_Student

general method for these problems.

Yes. The general method would be to use your brain. A radius of zero isn't going to give maximum volume.

Reply 25

Student403

Original post by Bath_Student

You absolute plonker. r=0 would be a perfectly feasible answer, if it weren't out of our man-made domain. OP needs to understand the general method for these problems.

And you've clearly stuck to that.

Original post by Bath_Student

If all understanding should fail, don't bother. Simply stick to r=4/3. It'll do, for now. Use that value to calculate the max volume, it's all the question ever really wanted.

Reply 26

username1258398

Original post by Bath_Student

Also, where's the display picture? Have we lost confidence in our "attractiveness"?

that'd be a fair point if you had a display picture yourself

Reply 27

frostyy

Original post by Bath_Student

I differentiated the former.
if v'= pi*r(4-3r)=4pi*r-3pi*r^2
then v''=4pi - 6pi*r = -2pi*(3r-2).

Now, second-derivative test. Did you even bother to read the article?

I did read it, but my 17 year old mind can't comprehend such an amount of f'(x) hieroglyphs.

I found the second-derivative and the value of r as 3/2. Do I use that in the final equation, or do I use the 4/3 from the first differentiation?

Reply 28

Bath_Student

Original post by Zacken

Yes. The general method would be to use your brain. A radius of zero isn't going to give maximum volume.

That is incorrect and problem-specific.

Optimisation problems require you to distinguish between the maximum and the minimum values by using the second derivative test. Admittedly here, a radius of 0 naturally must give the minimum value, which is why I eventually told OP "not to bother".

I also observe that the Cambridge cartel has arrived. Bunch of *****.

Reply 29

Student403

Original post by frostyy

Please ignore anything condescending he posts. You're doing fine :smile:

Reply 30

Bath_Student

Original post by frostyy

You must have found the wrong second derivative. Plugging 4/3 into the second derivative yields a negative value (such that the r value yields a maximum). IIRC, the value that comes from the second derivative was -4pi, proving that r=4/3 gives a maximum. Irrespective, take r=4/3 as your radius and plug it into V-equation.

Now then, if your fellow 17 year old mind could tell me how to get v, that'd be great.

Reply 31

Zacken

Original post by Bath_Student

Admittedly here, a radius of 0 naturally must give the minimum value, which is why I eventually told OP "not to bother.

Then why tell the other person to not speak if he knows nothing?

Reply 32

frostyy

Original post by Bath_Student

Now then, if your fellow 17 year old mind could tell me how to get v, that'd be great.

Not sure which 'v' you were asking for in that sentence, but confidence, bluntness and a tonne of lead up your ass is key :h:

Reply 33

Bath_Student

Original post by Zacken

Then why tell the other person to not speak if he knows nothing?

I get angry; it's the internet. I'm a nice guy irl. I hate intruders when I'm helping irl as well actually. I usually just get up and walk off.

I still maintain (as must you agree!) that these problems generally insist that you use the second derivative.

Reply 34

Bath_Student

Original post by frostyy

Confidence, bluntness and a tonne of lead up your ass :h:

haha, I've taken note.

What is the maximum value of v I can expect in a given year using your formula?

Reply 35

Zacken

Original post by Bath_Student

I would never use the second derivative to investigate the nature of the stationary point. Investigating the signs of the first derivative in a neighbourhood of your stationary point is all you need to determine the nature. This works even better than the second derivative as the latter can often lead to mis-conclusions, such as the nature of the stationary point for

x \mapsto x^4

Reply 36

Apolexian

Original post by frostyy

Not sure which 'v' you were asking for in that sentence, but confidence, bluntness and a tonne of lead up your ass is key :h:

Wow, that guy is touchy
even if you get two rs that are different, put the both into equation and pick the bigger V
dosnt take a genius

Reply 37

Bath_Student

Original post by Zacken

x \mapsto x^4

Original post by Apolexian

Wow, that guy is touchy
even if you get two rs that are different, put the both into equation and pick the bigger V
dosnt take a genius

All correct. From experience, though, mark schemes like secondary-deriving, if I may so say.

Reply 38

Apolexian

Original post by Bath_Student

keep quiet if you're don't know what you're on about.

You absolutely HAVE to do the second derivative test, because TWO values of r solved the above function, but only ONE yields a maximum! We were asked to find the maximum volume, NOT the minimum.

Have a read: http://mathworld.wolfram.com/SecondDerivativeTest.html

http://www.quickmeme.com/img/08/080ee2ca8c83f37fc4c66b5dc61d08b7b0defb398e26cf668d77a3380752d3eb.jpg

f0a1a0e1473bf5e5174b699b5d84d081b0bdc1b9820135c12453d93476157b39.jpg19.9KB

Reply 39

frostyy

can you just tell me what the answer is?