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10 Cards in this Set
- Front
- Back
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Evaluate: A=|a b| |c d| |
|A|= (ad)-(bc) |
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Equation to determine whether a CP is the location of a rel max, rel min, or saddle point |
D=fxx*fyy-(fxy)^2 |
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(a,b) is the location of a relative min if... |
D(a,b)>0 and fxx(a,b)>0 |
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(a,b) is the location of a relative max if... |
D(a,b)>0 and fxx(a,b)<0 |
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(a,b) is the location of a saddle point if... |
D(a,b)<0 |
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To locate candidates for relative extrema and saddle points |
1. Set each partial derivative equal to 0 and solve 2. Check to ensure the resulting ordered pairs are in the interior of the domain |
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Find A^(-1) A=|a b| |c d| |
A^(-1)=1/(ad-bc)|d -b| |-c a| |
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To locate candidates for relative extrema of f(x,y,...) subject to the constraint g(x,y,...)=0 |
1. Construct the Lagrangian Function: L(x,y,z)=f(x,y,...)-λg(x,y,...) 2. Set each partial derivative equal to 0 and solve |
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Cramer's Rule |
x=Dx/D, y=Dy/D, z=Dz/D... |
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Equation for the surface area of an open-top, rectangular container |
SA=2LH+2WH+LW |
