Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

minimum value

Find Minimum value of

Where

Last edited by juantheron (2012-01-18 03:50:57)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: minimum value

Hi juantheron;

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: minimum value

hi bobbym

i think this one is supposed to be graphed in the 3D coordinate system because it's a function of both x and y!

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“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: minimum value

I graphed it right over here which is designed for these type functions. But, you have a point.

---

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: minimum value

Thanks and Yes bobbym you are Right.

Now If anyone have a analytical solution plz post here.

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: minimum value

Hi juantheron;

I gave you one in post #2. It is hiding under the answer button. As anonimnystefy points out that graph only displays one slice of the actual graph. Anyway, I would never trust a graph unless I had no choice.

I will bring it down here.
Let me know if it is adequate.

For the analytical method you use calculus:

Set the partials of x and y equal to 0 and solve:

Those are the possible extrema.

Plug them into:

If Δ < 0 then we have neither a maximum or a minimum.

---

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: minimum value

Thanks Bobbym would you like to give me some idea about

Is it and Determinant

Last edited by juantheron (2012-01-19 03:38:46)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: minimum value

Hi juantheron;

I think you mean discriminant. But it isn't that either. I got it out of an old calculus text I will see if I can find the title.

---

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: minimum value

OK Thanks bobbym

But one of my friend told me that we can solve it like taking

, because

So It Convert into

So Here Leading Coefficient of

is Negative

so Minimum is not possible

Is it Right

Last edited by juantheron (2012-01-19 03:53:18)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: minimum value

I got mine from Smails, "Analytical Geometry and Calculus," p 564 in the middle.

I found it also at these sites:

http://www.math.oregonstate.edu/home/pr … n_max.html

http://www.analyzemath.com/calculus/mul … inima.html

He is right about that parabola not having a minima. Why does he use x = 2y to get 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.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: minimum value

I also did  not Understand

i also think that

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: minimum value

Hi juantheron;

Use mine then, it is a standard book idea.

---

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.