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anonymous
 5 years ago
Consider the function f(x,y)=5x−9y+4xy−7(x^2)+6(y^2) defined in the unit square 0</=x</=1, 0</=y</=1.
Find the maximum and minimum values of f and where they occur.
anonymous
 5 years ago
Consider the function f(x,y)=5x−9y+4xy−7(x^2)+6(y^2) defined in the unit square 0</=x</=1, 0</=y</=1. Find the maximum and minimum values of f and where they occur.

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0it appears to be hyperbolic ......

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we can get a vector derivative if we take the gradient: but I aint sure how that would help yet

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(x,y)=5x−9y+4xy−7(x^2)+6(y^2) fx(x,y) = 5 +4y 14x fy(x,y) = 9 +4x +12y

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0gf = (5 +4y 14x , 9 +4x +12y) can also define the normal to the surface; when this is pointing straight up or down would give you a tangent plane for a min or max right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0straight up is the same as (0,y); so id say make x=0 for starters ... just a hunch

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0gf = (5 +4y , 9 +12y)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that mighta been a wrong step lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0gf = (5 +4y 14x , 9 +4x +12y) maybe when 5 +4y 14x = 0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't remember how to do this.. but we dealing with a gradient mic in one of my classes

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0mic check one two one two

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.05 +4y 14x = 0 y = 14x5 x = 4y +5   4 14

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can you use LaTeX here?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when: 5 +4y 14x = 9 +4x +12y we might get a zero derivative.... 5 + 4y 14x 9 12y 4x  14 8y 18x = 0 18x +8y = 14 ... i wonder...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=5x%E2%88%929y%2B4xy%E2%88%927%28x^2%29%2B6%28y^2%29

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i was sooo close lol add the gradient parts and do something....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i was on the right track; when the x and y parts of the gradient =0 we got a tangent plane that is flat.... to indicate a high and low

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.018x +8y = 14; we can use values between 0 and 1 to find out what works now

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the line y=(18x+14)/8 should give us the answers right? or y = (9x+7)/4
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