I didi it it!Originally posted by haditya@Oct 7 2005, 05:00 AM
one easy way to find this out would be to find maxima -minima using derivatives
since its a a function of two independent variables
the following conditions are to be satisfied:-
∂ f/ ∂ x = 0
∂ f/ ∂ y = 0
this will give you the pair of critical points(x,y) where optima may exist
let r= ∂ ^2 f/ ∂x^2 ; s= ∂ ^2 f/ ∂y^2; t= ∂ ^2 f/ ∂x ∂ y;
substituting each of the above critical points into the second order derivatives we check for the following conditions:
1. rt-s*s <0 no maxima or minima
2. rt-s*s > 0 => maxima if r<0; minima r>0
3. rt-s*s = 0 => test is inconclusive and an alternate means must be established
try attemptin a solution using this fact
[post=10846]Quoted post[/post]
Originally posted by haditya@Oct 7 2005, 11:00 AM
one easy way to find this out would be to find maxima -minima using derivatives
since its a a function of two independent variables
the following conditions are to be satisfied:-
∂ f/ ∂ x = 0
∂ f/ ∂ y = 0
this will give you the pair of critical points(x,y) where optima may exist
let r= ∂ ^2 f/ ∂x^2 ; s= ∂ ^2 f/ ∂y^2; t= ∂ ^2 f/ ∂x ∂ y;
substituting each of the above critical points into the second order derivatives we check for the following conditions:
1. rt-s*s <0 no maxima or minima
2. rt-s*s > 0 => maxima if r<0; minima r>0
3. rt-s*s = 0 => test is inconclusive and an alternate means must be established
try attemptin a solution using this fact
[post=10846]Quoted post[/post]
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