Thinking about the shape of the graph (no calulus needed), what is the largest
value of f(x,y) = 1/(1+x^2+y^4)?

Well this one is easy, is obviously that f(0,0) = 1 is the highest value.
Otherwise if x or y increase in any direction from the origin (positive or negative), f will decrease exponenttialy.

Originally Posted by apatite
Thinking about the shape of the graph (no calulus needed), what is the largest
value of f(x,y) = 1/(1+x^2+y^4)?
If no calculus is needed, then why on earth are you posting in 'calculus'?

Originally Posted by Paze
If no calculus is needed, then why on earth are you posting in 'calculus'?
That thought occurred to me, too.

Assuming x and y are real numbers, x^2 and y^4 are nonnegative, so the largest possible value is clearly f(x,y)=1 at (x,y)=(0,0) as draganicimw observed. One rather trivial correction - f does not decrease exponentially away from the origin; its decrease is only polynomial.

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