Thinking about the shape of the graph (no calculus needed) what is the largest value of f(x,y)=1/(1+x^2+y^4)?
The largest value of f(x,y) will occur when denominator has its minimal value. The denominator is 1+x^2+y^4 and since x^2 andy^4 always >=0, the denominator has the minimal value when x=0 and y=0. So, the largest value of this function is f(0,0)=1/(1+0^2+0^4)=1/1=1
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