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boombastictiger

Member

Registered: 2005-08-28

Posts: 10

Partial Derivative help...

I have a basic question I am stuck on...

Given the function Z= ln(y /x) Find the partial derivatives:

(A) dz/dx

(B) dz/dy

(C) Given the function, z=x³ + xy + y², show that (0,0) and (1/6, - 1/12) the only stationary points and classify them (that is, decide whether these points are maximum or minimum or saddle points).

Edited i added a comma after 1/6 it makes a big difference sorry...

Last edited by boombastictiger (2008-08-24 02:44:50)

boombastictiger

Member

Registered: 2005-08-28

Posts: 10

Re: Partial Derivative help...

no one can answer these ?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Partial Derivative help...

Start off by rewriting the function as Z = ln(y) - ln(x), using laws of logs.

Looking at the function that way, finding the two partial derivatives shouldn't pose any problem for you.

For c), start off by finding the partial derivatives with respect to x and y again.
For example, dZ/dx = 3x² + y (+0).

Once you have dZ/dy as well, setting them both equal to 0 will get you two simultaneous equations, which should solve to give you those two stationary points. (I suggest making y the subject of both equations, then setting them equal to each other and solving for x)

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Why did the vector cross the road?
It wanted to be normal.