perplexus.info :: Calculus : Maximal of a function

Maximal of a function (Posted on 2020-11-25)

Show that there exists the maximum value of the function f(x, y)=(3xy+1)e^-(x²+y²) on R², then find the value.

No Solution Yet Submitted by Danish Ahmed Khan

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No proof, but approx max found

| Comment 1 of 2

a=zeros(200); mx=0;

for x=- .9:.01:.9

for y=- .9:.01: .9

v=(3*x*y+1)*exp(-x^2-y^2);

a(round((x+1)*100),round((y+1)*100))=v;

if v>mx mx=v; mxx=x; mxy=y; end

end

disp([mx,mxx,mxy])

mx=0;

for x=.4:.0000000001:.41

v=(3*x*x+1)*exp(-x^2-x^2);

if v>mx mx=v;mxx=x;

end

disp([mx,mxx])

The max is about 1.07479696586068 for x=y= 0.4082482808

and the same for x=y= - 0.4082482808

Posted by Charlie on 2020-11-25 14:24:53

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