Problems on maxima and minima (1 Viewer)

[apak]

I would just like to double check, when doing maximum and minimum points. A typical example would be Find the overall dimemsion if the totall area.......TO BE A MINIMUM. Normally what i do just just dy/dx - sub it in and etc. i get the answer and its normally correct. My question is - IF THE QUESTION ASKS FOR A MINIMUM WILL YOU ANSWER BE A MINIMUM and the same for maximum?

Thanks in adv

p.s im sorry if this is a 2u question. When your taught 3u you just dont know which part of it is 2u...

 

[acmilan]

If you have dy/dx, you need to solve it by making it equal to 0. I dont know what you mean by subbing something into it :S For those area type questions, dy/dx will most likely have 2 solutions when you make it equal 0, you then need to test these solutions to see which ones a max and which is a min. Also, you can just assume that because there is only one solution that it is always gonna be what you need, an equation may sometimes not have a minimum turning point at all.

I think thats what you mean, sorry if i interpreted your question wrong

 

[apak]

im not exactly talking about curves and where it turns. im talking about area's of rectangles shapes and etc. in these question dy/dx only has 1 answer

 

[acmilan]

Yes, but you cant assume the answer is what you need, you need to test it always.

 

[apak]

i dont exactly get you. but for example in the question
A rectangle has perimeter of 32m. find the max area.
(x) (16-x) = 32
16x -x^2 = 32
dy/dx = -2x + 16
dy/dx = 0 then 2x = 16 x=8
in this question there is only 1 answer which is a maximum . i would like know does this apply for all max and min question - that there is only 1 answer

 

[acmilan]

Not necessarily, but most likely it would. It all depends on what the criteria is and the relationship between the sides.

 

[apak]

thx - i now conclude it depends on the equation