Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

Maximumvalue

Maximum value of function

where

Last edited by juantheron (2012-04-07 21:54:12)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maximumvalue

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Maximumvalue

hi

I am getting

Bob

---

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maximumvalue

Hi Bob;

Sorry, I wrote 1 / 3 when I meant 2 / 3. I edited it to correct it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Maximumvalue

Oh wow!

I think I may just have corrected you. 

That's made my day!!  (Yes, I know I'm easily pleased ....)

Do you think he'd like the method?

Bob

---

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maximumvalue

Hi;

I have become somewhat thick skinned about corrections, since it happens to me 10^40 times a day.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Maximumvalue

10^40 times a day.

There aren't enough seconds.  I think this may need correcting.

Bob

---

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maximumvalue

10^40, I call that anonimnystefy's number since it popped up in the "Whats my Line" thread.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: Maximumvalue

Thanks Moderators, but I want explanation for that answer

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maximumvalue

I did mine by Calculus. The differentiations were tough and I used a computer to do them.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Maximumvalue

I did on a piece of paper so I'll transcribe it now and edit this post as I go

I think this is finished.  I'm just checking now.

DONE!

partially differentiate wrt x (treat y as constant)

and similarly for y

Set each equal to zero.

Then solve these simultaneously (numerators must be zero)

and

Subtract to eliminate 6y

note x = 0 is not possible so it can be cancelled

then x = 1

Strictly I should also prove this is a maximum, not anything else.  Probably the easiest way is to substitute a couple of values just to the side (one x wise and the other y wise) and observe a lower value for Z in each case.  that eliminates a minimum and a saddle point.

Bob

---

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Maximumvalue

10^40, I call that anonimnystefy's number since it popped up in the "Whats my Line" thread.

Why thank you,bobbym. I have got my own number now,but you have it wrong. My number is 10^40-1.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maximumvalue

Depends on your point of view. 10^40 is yours now, I afraid you are stuck with it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Maximumvalue

hi juantheron,

post 11 is now finished.

Bob

---

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maximumvalue

Hi;

I generally use values on either side of the extrema. This is usually sufficient for technical work. For more rigor you must use the formula:

Substituting in the point:

Now because Δ > 0 and one second derivative is < 0 we have a maximum.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

sameer mishra

Member

Registered: 2010-08-27

Posts: 64

Re: Maximumvalue

obtain partial differential of above function w.r.t x&y equals it to be zero from here obtain value of x,y then obtain f" if it is less than zero then maxima will exist at that coordinate.