Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Maxima and minima

A fun little question which I'm afraid has got me stumped. I'm not really sure how to approach this, what do you think?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Maxima and minima

hi Au101,

I think the formula would be something like:

The given values should be enough to calculate the constants j, k and L.

Then you can differentiate to get the turning points, and show the one you find is a minimum, not a maximum.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Maxima and minima

Thanks a lot! That seems to've done the trick

I was about halfway there, but I hadn't quite fully understood the question.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Maxima and minima

Hopefully, that's what the questioner had in mind.  The graph cost against V will have a minimum so you should be able to solve this now.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Maxima and minima

Yeah - well, certainly, the answer checks out (26 when rounded appropriately).

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Maxima and minima

The final question of this exercise is (in my opinion) another slightly fiendish one. Again, there's something I'm just not getting. Here it is:

For what it's worth, I've worked out that the gradient (call it m) of the line is:

But I can't say I've had any more breakthroughs than that.

I wondered briefly whether the least value of OA + OB will occur when the gradient is -1. If that's true I haven't been able to prove it, or get anywhere by taking that as a starting point!

Last edited by Au101 (2015-02-10 11:08:30)

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Maxima and minima

If the gradient of the line is m (<0) its equation is

. Now find OA and OB in terms of m, a and b.

The problem is now to treat m as a variable find the value of it that minimizes OA+OB.

Similarly for the triangle, find the value of m that minimizes (OA·OB)/2.

Last edited by Olinguito (2015-02-10 21:29:39)

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Bassaricyon neblina

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Maxima and minima

Thank you very much Olinguito, that's got it, I just needed help with how to think about it