Just a reality check. It is SO CLOSE to "exact" that I am first inclined to make sure there is not just a typo.
Hi,
my name is Dimos and I am coming from Greece.
Right to the point.
1) Can somebody help me with the:
ODE?
I ve tried to find a integration factor and change variable (e.g. v=2x*cos(y) ). I have no clue! Is this ODE a suitable example for polytechnics student?
2) Is there any higher order derivative test to find extrema of multi variable functions? Where can i find more details?
3) Can the use of Lagrange multipliers reveal the nature of extrema (i.e. is it a local minimum, local maximum or saddle point)? How?
Thank you in advance for any help!
Dimos
Athens.
I thought it was a typo. If x in the dy/dx term was sin(x), the ODE would be exact and having the solution
the person gave it to me for solving is not available at the moment. So I assumed it s correct.
Anyway it may be an interesting (and hard to solve) ODE.
Thanks for your help TKHunny!
Dimos
Do you know about the second partials test?
Source: Calculus : Multivariable by Anton, Bivens, Davis. 8th Ed.THEOREM: Second Partials Test.
Let be a function of two variables with continuous second order partial derivatives in some disk centered at a critical point , and let
(a) If and , then has a relative minimum at
(b) If and , then has a relative maximum at
(c) If , then has a saddle point at
(d) If , then no conclusion can be drawn
Yes you can show these things. I don't have the time to go through the process, but you need to use this equation(s):3) Can the use of Lagrange multipliers reveal the nature of extrema (i.e. is it a local minimum, local maximum or saddle point)? How?
<---Use when you have two variables and one constraint.
<---Use when you have three variables and one constraint.
where is the Lagrange Multiplier.
I hope this helps!
--Chris